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<div class="tableofcontents">
<h3>Contents</h3>
<div class="toc">
<div class="h2"><a href="#most-popular"> Most Popular Geometry Worksheets this Week</a></div>
<div class="h2"><a href="#lines-angles">Lines and Angles</a></div>
<div class="h2"><a href="#shapes">Triangles, Quadrilaterals and Other Shapes</a></div>
<div class="h2"><a href="#coordinate-plane">Coordinate Plane Worksheets</a></div>
<div class="h2"><a href="#transformations">Transformations Worksheets</a></div>
<div class="h2"><a href="#constructions">Constructions Worksheets</a></div>
<div class="h2"><a href="#three-dimensional-geometry">Three-Dimensional Geometry</a></div>
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<p class="firstp">Welcome to the geometry worksheets page at Math-Drills.com where we believe that there is nothing wrong with being square! This page includes <span itemprop="description">Geometry Worksheets on angles, coordinate geometry, triangles, quadrilaterals, transformations and three-dimensional geometry worksheets.</span></p>
<p>Get out those rulers, protractors and compasses because we've got some great worksheets for geometry! The quadrilaterals are meant to be cut out, measured, folded, compared, and even written upon. They can be quite useful in teaching all sorts of concepts related to quadrilaterals. Just below them, you'll find worksheets meant for angle geometry. Also see the measurement page for more angle worksheets. The bulk of this page is devoted to transformations. Transformational geometry is one of those topics that can be really interesting for students and we've got enough worksheets for that geometry topic to keep your students busy for hours.</p>
<p>Don't miss the challenging, but interesting world of connecting cubes at the bottom of this page. You might encounter a few future artists when you use these worksheets with students.</p>
<div class="popular">
<h2 id="most-popular"><svg class="iconwhite size32 iorange"><use xlink:href="includes/symbol-defs.006.svg#icon-fire"></use></svg> Most Popular Geometry Worksheets this Week</h2>
<div class="searchresults">
<a href="geometry/geometry_comsup_angles_rotated_001.html" title="Complementary and Supplementary Angle Relationships with Rotated Diagrams"><figure><img src="geometry/images/geometry_comsup_angles_rotated_001_300.1705165645.jpg" alt="Complementary and Supplementary Angle Relationships with Rotated Diagrams" loading="lazy" width="250" height="324"><figcaption>Complementary and Supplementary Angle Relationships with Rotated Diagrams (<strong>510 views this week</strong>)</figcaption></figure></a>
<a href="geometry/coordinate_point_plots_001.html" title="Plotting Coordinate Points"><figure><img src="geometry/images/coordinate_point_plots_001_300.1675735269.jpg" alt="Plotting Coordinate Points" loading="lazy" width="250" height="324"><figcaption>Plotting Coordinate Points (<strong>481 views this week</strong>)</figcaption></figure></a>
<a href="geometry/geometry_identify_lines_segments_rays_001.html" title="Identifying Lines, Line Segments and Rays"><figure><img src="geometry/images/geometry_identify_lines_segments_rays_001_300.1702837734.jpg" alt="Identifying Lines, Line Segments and Rays" loading="lazy" width="250" height="324"><figcaption>Identifying Lines, Line Segments and Rays (<strong>269 views this week</strong>)</figcaption></figure></a>
<a href="geometry/scale_factor_trirectangles_half_intervals_001.html" title="Determine the Scale Factor Between Two Shapes and Determine the Missing Lengths (Scale Factors in Intervals of 0.5)"><figure><img src="geometry/images/scale_factor_trirectangles_half_intervals_001_300.1675735270.jpg" alt="Determine the Scale Factor Between Two Shapes and Determine the Missing Lengths (Scale Factors in Intervals of 0.5)" loading="lazy" width="250" height="324"><figcaption>Determine the Scale Factor Between Two Shapes and Determine the Missing Lengths (Scale Factors in Intervals of 0.5) (<strong>259 views this week</strong>)</figcaption></figure></a>
<a href="geometry/coordinate_point_art_001.html" title="Plotting Coordinate Points Art -- Red Maple Leaf"><figure><img src="geometry/images/coordinate_point_art_001_300.1360946745.jpg" alt="Plotting Coordinate Points Art -- Red Maple Leaf" loading="lazy" width="250" height="324"><figcaption>Plotting Coordinate Points Art -- Red Maple Leaf (<strong>252 views this week</strong>)</figcaption></figure></a>
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<h2 id="lines-angles">Lines and Angles</h2>
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<div class="imagearea">
<img src="geometry/images/geometry_naming_simple_angles_001_300.004.jpg" alt="" width="250" height="324" loading="lazy">
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<div class="worksheetsarea">
<ul class="list">
<li><p>In this section, there are worksheets for two of the basic concepts of geometry: lines and angles.</p></li>
<li><p>Lines (or straight lines to be precise) in geometry are continuous and extend in both directions to infinity. They have no width, depth or curvature. In math activities, they are often represented by a drawn straight path with some width. To show that they are lines, arrows are drawn on each end to show they extend to infinity. A line segment is a finite section of a line. Line segments are often represented with points at each end of a drawn straight path. Rays start at a point and extend in a straight line to infinity. This is shown with a point at one end of a drawn straight path and an arrow at the other end.</p></li>
<li><input type="checkbox" class="list-checkbox" id="lines-angles-1"><label for="lines-angles-1" class="wtitle">Identifying Lines, Line Segments and Rays</label>
<div class="desc">
<a href="geometry/geometry_identify_lines_segments_rays_001.html" class="">Identify Lines, Segments and Rays</a>
</div>
</li>
<li><p>Angles can be classified into six different types. Acute angles are greater than 0 degrees but less than 90 degrees. Right angles are exactly 90 degrees. Obtuse angles are greater than 90 degrees but less than 180 degrees. Straight angles are exactly 180 degrees. Reflex angles are greater than 180 degrees but less than 360 degrees. Complete/Full angles are exactly 360 degrees.</p></li>
<li><input type="checkbox" class="list-checkbox" id="lines-angles-2"><label for="lines-angles-2" class="wtitle">Identifying Angle Types Worksheets</label>
<div class="desc">
<a href="geometry/geometry_identify_angles_acute_obtuse_marks_001.html" class="">Identifying Acute and Obtuse Angles</a>
<a href="geometry/geometry_identify_angles_acute_obtuse_nomarks_001.html" class="">Identifying Acute and Obtuse Angles (No Angle Marks)</a>
<a href="geometry/geometry_naming_simple_angles_001.html" class="">Identifying Acute, Obtuse and Right Angles</a>
<a href="geometry/geometry_identify_angles_acute_obtuse_right_nomarks_001.html" class="">Identifying Acute, Obtuse and Right Angles (No Angle Marks)</a>
<a href="geometry/geometry_identify_angles_acute_obtuse_right_straight_marks_001.html" class="">Identifying Acute, Obtuse, Right and Straight Angles</a>
<a href="geometry/geometry_identify_angles_acute_obtuse_right_straight_nomarks_001.html" class="">Identifying Acute, Obtuse, Right and Straight Angles (No Angle Marks)</a>
<a href="geometry/geometry_naming_all_angles_001.html" class="">Identifying Acute, Obtuse, Right, Straight and Reflex Angles</a>
<a href="geometry/geometry_identify_angles_acute_obtuse_right_straight_reflex_complete_marks_001.html" class="">Identifying Acute, Obtuse, Right, Straight, Reflex and Complete/Full Angles</a>
</div>
</li>
<li><p>There are several angle relationships of which students should be aware. <strong>Complementary angles</strong> are two angles that together form a 90 degree angle; <strong>supplementary angles</strong> are two angles that together form a 180 degree angle; and <strong>explementary angles</strong> are two angles that together form a 360 degree angle. <strong>Vertical angles</strong> are found at line intersections; angles opposite each other are equal. Students can practice determining and/or calculating the unknown angle(s) in the following angle relationships worksheets.</p></li>
<li><input type="checkbox" class="list-checkbox" id="lines-angles-3"><label for="lines-angles-3" class="wtitle">Angle Relationships Worksheets</label>
<div class="desc">
<a href="geometry/geometry_complementary_angles_001.html" class="">Complementary Angles</a>
<a href="geometry/geometry_complementary_angles_rotated_001.html" class="">Complementary Angles (Diagrams Rotated)</a>
<a href="geometry/geometry_supplementary_angles_001.html" class="">Supplementary Angles</a>
<a href="geometry/geometry_supplementary_angles_rotated_001.html" class="">Supplementary Angles (Diagrams Rotated)</a>
<a href="geometry/geometry_comsup_angles_rotated_001.html" class="">Mixed Complementary and Supplementary Angles Questions (Diagrams Rotated)</a>
<a href="geometry/geometry_explementary_angles_001.html" class="">Explementary Angles</a>
<a href="geometry/geometry_explementary_angles_rotated_001.html" class="">Explementary Angles (Diagrams Rotated)</a>
<a href="geometry/geometry_adjacent_angles_rotated_001.html" class="">Mixed Adjacent Angles Questions (Diagrams Rotated)</a>
<a href="geometry/geometry_vertical_angles_001.html" class="">Vertical/Opposite Angles</a>
<a href="geometry/geometry_vertical_angles_rotated_001.html" class="">Vertical/Opposite Angles (Diagrams Rotated)</a>
<a href="geometry/geometry_comsupexop_angles_rotated_001.html" class="">Mixed Angle Relationships Questions(Diagrams Rotated)</a>
</div>
</li>
<li><input type="checkbox" class="list-checkbox" id="lines-angles-4"><label for="lines-angles-4" class="wtitle">Angles of Transversals Intersecting Parallel Lines</label>
<div class="desc">
<a href="geometry/geometry_interior_alternate_angles_001.html" class="">Interior Alternate Angles</a>
<a href="geometry/geometry_exterior_alternate_angles_001.html" class="">Exterior Alternate Angles</a>
<a href="geometry/geometry_alternate_angles_001.html" class="">Alternate Angles</a>
<a href="geometry/geometry_corresponding_angles_001.html" class="">Corresponding Angles</a>
<a href="geometry/geometry_co-interior_angles_001.html" class="">Co-Interior Angles</a>
<a href="geometry/geometry_transversals_001.html" class="">Transversals</a>
</div>
</li>
<li><p>Measuring angles worksheets, can be found on the <a href="measurement.html" class="inlinelink pi">Measurement Page</a></p></li>
</ul>
</div>
</div>
<div class="wscontainer bc01">
<div class="titlearea">
<h2 id="shapes">Triangles, Quadrilaterals and Other Shapes</h2>
</div>
<div class="imagearea">
<img src="geometry/images/triangles_classifying_mixed_001_300.004.jpg" alt="" width="250" height="324" loading="lazy">
</div>
<div class="worksheetsarea">
<ul class="list">
<li><p>The quadrilaterals set can be used for a number of activities that involve classifying and recognizing quadrilaterals or for finding the properties of quadrilaterals (e.g. that the interior angles add up to 360 degrees). The tangram printables are useful in tangram activities. There are several options available for the tangram printables depending on your printer, and each option includes a large version and smaller versions. If you know someone with a suitable saw, you can use the tangram printable as a template on material such as quarter inch plywood; then simply sand and paint the pieces.</p></li>
<li><input type="checkbox" class="list-checkbox" id="shapes-5"><label for="shapes-5" class="wtitle">Shape Sets</label>
<div class="desc">
<a href="geometry/geometry_quadrilaterals_set.html" class="">Quadrilaterals Set</a>
<a href="geometry/tangrams_all.html" class="">Tangrams</a>
</div>
</li>
<li><input type="checkbox" class="list-checkbox" id="shapes-6"><label for="shapes-6" class="wtitle">Identifying Regular Polygons</label>
<div class="desc">
<a href="geometry/shapes_identify_regular_triangle_to_octagon_001.html" class="">Identifying Regular Shapes from Triangles to Octagons</a>
</div>
</li>
<li><p>Worksheets for classifying triangles by side and angle properties and for working with Pythagorean theorem.</p></li>
<li><p>If you are interested in students measuring angles and sides for themselves, it is best to use the versions with no marks. The marked versions will indicate the right and obtuse angles and the equal sides.</p></li>
<li><input type="checkbox" class="list-checkbox" id="shapes-7"><label for="shapes-7" class="wtitle">Classifying Triangles Worksheets</label>
<div class="desc">
<a href="geometry/triangles_classifying_side_001.html" class="">Classifying Triangles <strong>by Side Properties</strong></a>
<a href="geometry/triangles_classifying_angle_001.html" class="">Classifying Triangles <strong>by Angle Properties</strong></a>
<a href="geometry/triangles_classifying_mixed_001.html" class="">Classifying Triangles <strong>by Side and Angle Properties</strong></a>
<a href="geometry/triangles_classifying_side_nomarks_001.html" class="">Classifying Triangles <strong>by Side Properties (No Marks)</strong></a>
<a href="geometry/triangles_classifying_angle_nomarks_001.html" class="">Classifying Triangles <strong>by Angle Properties (No Marks)</strong></a>
<a href="geometry/triangles_classifying_mixed_nomarks_001.html" class="">Classifying Triangles <strong>by Side and Angle Properties (No Marks)</strong></a>
</div>
</li>
<li><p>A cathetus (plural catheti) refers to a side of a right-angle triangle other than the hypotenuse.</p></li>
<li><input type="checkbox" class="list-checkbox" id="shapes-8"><label for="shapes-8" class="wtitle">Calculating Triangle Dimensions Using Pythagorean Theorem</label>
<div class="desc">
<a href="geometry/pythagorean_theorem_decimal_calculate_hypotenuse_norotation_001.html" class="">Calculate the <strong>Hypotenuse</strong> Using Pythagorean Theorem <strong>(No Rotation)</strong></a>
<a href="geometry/pythagorean_theorem_decimal_calculate_hypotenuse_rotation_001.html" class="">Calculate the <strong>Hypotenuse</strong> Using Pythagorean Theorem</a>
<a href="geometry/pythagorean_theorem_decimal_calculate_cathetus_norotation_001.html" class="">Calculate a <strong>Cathetus</strong> Using Pythagorean Theorem <strong>(No Rotation)</strong></a>
<a href="geometry/pythagorean_theorem_decimal_calculate_cathetus_rotation_001.html" class="">Calculate a <strong>Cathetus</strong> Using Pythagorean Theorem</a>
<a href="geometry/pythagorean_theorem_decimal_calculate_side_norotation_001.html" class="">Calculate any <strong>Side</strong> Using Pythagorean Theorem <strong>(No Rotation)</strong></a>
<a href="geometry/pythagorean_theorem_decimal_calculate_side_rotation_001.html" class="">Calculate any <strong>Side</strong> Using Pythagorean Theorem</a>
</div>
</li>
<li><p>Trigonometric ratios are useful in determining the dimensions of right-angled triangles. The three basic ratios are summarized by the acronym SOHCAHTOA. The SOH part refers to the ratio: sin(α) = O/H where α is an angle measurement; O refers the length of the side (O)pposite the angle measurement and H refers to the length of the (H)ypotenuse of the right-angled triangle. The CAH part refers to the ratio: cos(α) = A/H where A refers to the length of the (A)djacent side to the angle. The TOA refers to the ratio: tan(α) = O/A.</p></li>
<li><input type="checkbox" class="list-checkbox" id="shapes-9"><label for="shapes-9" class="wtitle">Calculating Angles and Sides Using Trigonometric Ratios</label>
<div class="desc">
<a href="geometry/trigonometry_sohcahtoa_sine_ratio_angles_001.html" class="">Calculating <strong>Angles</strong> Using the <strong>Sine Ratio</strong></a>
<a href="geometry/trigonometry_sohcahtoa_sine_ratio_sides_001.html" class="">Calculating <strong>Sides</strong> Using the <strong>Sine Ratio</strong></a>
<a href="geometry/trigonometry_sohcahtoa_sine_ratio_both_001.html" class="">Calculating <strong>Angles and Sides</strong> Using the <strong>Sine Ratio</strong></a>
<a href="geometry/trigonometry_sohcahtoa_cosine_ratio_angles_001.html" class="">Calculating <strong>Angles</strong> Using the <strong>Cosine Ratio</strong></a>
<a href="geometry/trigonometry_sohcahtoa_cosine_ratio_sides_001.html" class="">Calculating <strong>Sides</strong> Using the <strong>Cosine Ratio</strong></a>
<a href="geometry/trigonometry_sohcahtoa_cosine_ratio_both_001.html" class="">Calculating <strong>Angles and Sides</strong> Using the <strong>Cosine Ratio</strong></a>
<a href="geometry/trigonometry_sohcahtoa_tangent_ratio_angles_001.html" class="">Calculating <strong>Angles</strong> Using the <strong>Tangent Ratio</strong></a>
<a href="geometry/trigonometry_sohcahtoa_tangent_ratio_sides_001.html" class="">Calculating <strong>Sides</strong> Using the <strong>Tangent Ratio</strong></a>
<a href="geometry/trigonometry_sohcahtoa_tangent_ratio_both_001.html" class="">Calculating <strong>Angles and Sides</strong> Using the <strong>Tangent Ratio</strong></a>
<a href="geometry/trigonometry_sohcahtoa_trigonometric_ratios_angles_001.html" class="">Calculating <strong>Angles</strong> Using <strong>Trigonometric Ratios</strong></a>
<a href="geometry/trigonometry_sohcahtoa_trigonometric_ratios_sides_001.html" class="">Calculating <strong>Sides</strong> Using <strong>Trigonometric Ratios</strong></a>
<a href="geometry/trigonometry_sohcahtoa_trigonometric_ratios_both_001.html" class="">Calculating <strong>Angles and Sides</strong> Using <strong>Trigonometric Ratios</strong></a>
</div>
</li>
<li><p>Quadrilaterals are interesting shapes to classify. Their classification relies on a few attributes and most quadrilaterals can be classified as more than one shape. A square, for example, is also a parallelogram, rhombus, rectangle and kite. A quick summary of all quadrilaterals is as follows: quadrilaterals have four sides. A square has 90 degree corners and equal length sides. A rectangle has 90 degree corners, but the side lengths don't have to be equal. A rhombus has equal length sides, but the angles don't have to be 90 degrees. A parallelogram has both pairs of opposite sides equal and parallel and both pairs of opposite angles are equal. A trapezoid only needs to have one pair of opposite sides parallel. A kite has two pairs of equal length sides where each pair is joined/adjacent rather than opposite to one other. A bowtie is sometimes included which is a complex quadrilateral with two sides that crossover one another, but they are readily recognizable. Any other four-sided polygon can safely be called a quadrilateral if it doesn't meet any of the criteria for a more specific classification.</p></li>
<li><input type="checkbox" class="list-checkbox" id="shapes-10"><label for="shapes-10" class="wtitle">Classifying Quadrilaterals</label>
<div class="desc">
<a href="geometry/quadrilaterals_classify_simple_001.html" class="">Classifying Simple Quadrilaterals</a>
<a href="geometry/quadrilaterals_classify_allquad_001.html" class="">Classifying All Quadrilaterals</a>
<a href="geometry/quadrilaterals_classify_001.html" class="">Classifying All Quadrilaterals (+ Rotation)</a>
</div>
</li>
</ul>
</div>
</div>
<div class="wscontainer bc01">
<div class="titlearea">
<h2 id="coordinate-plane">Coordinate Plane Worksheets</h2>
</div>
<div class="imagearea">
<img src="geometry/images/coordinate_point_plots_001_300.004.jpg" alt="" width="250" height="324" loading="lazy">
</div>
<div class="worksheetsarea">
<ul class="list">
<li><p>Coordinate point geometry worksheets to help students learn about the Cartesian plane.</p></li>
<li><input type="checkbox" class="list-checkbox" id="coordinate-plane-11"><label for="coordinate-plane-11" class="wtitle">Plotting Random Coordinate Points</label>
<div class="desc">
<a href="geometry/coordinate_point_plots_001.html" class="">Plotting Coordinate Points in All Quadrants</a>
<a href="geometry/coordinate_point_plots_x_001.html" class="">Plotting Coordinate Points in Positive <i>x</i> Quadrants</a>
<a href="geometry/coordinate_point_plots_y_001.html" class="">Plotting Coordinate Points in Positive <i>y</i> Quadrants</a>
</div>
</li>
<li><p>There are many other Cartesian Art plots scattered around the Math-Drills website as many of them are associated with a holiday. To find them quickly, use the search box.</p></li>
<li><input type="checkbox" class="list-checkbox" id="coordinate-plane-12"><label for="coordinate-plane-12" class="wtitle">Cartesian Art</label>
<div class="desc">
<a href="geometry/coordinate_point_art_001.html" class="">Cartesian Art Maple Leaf</a>
</div>
</li>
<li><input type="checkbox" class="list-checkbox" id="coordinate-plane-13"><label for="coordinate-plane-13" class="wtitle">Coordinate Plane Distance and Area</label>
<div class="desc">
<a href="geometry/coordinate_plane_pythagorean_distance_001.html" class="">Calculating Pythagorean Distances of Coordinate Points</a>
<a href="geometry/coordinate_plane_perimeter_area_triangles_001.html" class="">Calculating Perimeter and Area of Triangles on Coordinate Planes</a>
<a href="geometry/coordinate_plane_perimeter_area_quadrilaterals_001.html" class="">Calculating Perimeter and Area of Quadrilaterals on Coordinate Planes</a>
<a href="geometry/coordinate_plane_perimeter_area_mixed_001.html" class="">Calculating Perimeter and Area of Triangles and Quadrilaterals on Coordinate Planes</a>
</div>
</li>
</ul>
</div>
</div>
<div class="wscontainer bc01">
<div class="titlearea">
<h2 id="transformations">Transformations Worksheets</h2>
</div>
<div class="imagearea">
<img src="geometry/images/translations_3points_3units_001_300.004.jpg" alt="" width="250" height="324" loading="lazy">
</div>
<div class="worksheetsarea">
<ul class="list">
<li><p>Transformations worksheets for translations, reflections, rotations and dilations practice.</p></li>
<li><p>Here are two quick and easy ways to check students' answers on the transformational geometry worksheets below. First, you can line up the student's page and the answer page and hold it up to the light. Moving/sliding the pages slightly will show you if the student's answers are correct. Keep the student's page on top and mark it or give feedback as necessary. The second way is to photocopy the answer page onto an overhead transparency. Overlay the transparency on the student's page and flip it up as necessary to mark or give feedback.</p></li>
<li><p>Also known as sliding, translations are a way to mathematically describe how something moves on a Cartesian plane. In translations, every vertex and line segment moves the same, so the resulting shape is congruent to the original.</p></li>
<li><input type="checkbox" class="list-checkbox" id="transformations-14"><label for="transformations-14" class="wtitle">Translations Worksheets</label>
<div class="desc">
<a href="geometry/translations_3points_3units_001.html" class="">Translation of 3 vertices by up to 3 units.</a>
<a href="geometry/translations_3points_6units_001.html" class="">Translation of 3 vertices by up to 6 units.</a>
<a href="geometry/translations_3points_25units_001.html" class="">Translation of 3 vertices by up to 25 units.</a>
<a href="geometry/translations_4points_6units_001.html" class="">Translation of 4 vertices by up to 6 units.</a>
<a href="geometry/translations_5points_6units_001.html" class="">Translation of 5 vertices by up to 6 units.</a>
</div>
</li>
<li><input type="checkbox" class="list-checkbox" id="transformations-15"><label for="transformations-15" class="wtitle">Translations Worksheets (Multi-Step)</label>
<div class="desc">
<a href="geometry/translations_3points_6units_2step_001.html" class=""><strong>Two-Step</strong> Translation of 3 vertices by up to 6 units.</a>
<a href="geometry/translations_4points_6units_2step_001.html" class=""><strong>Two-Step</strong> Translation of 4 vertices by up to 6 units.</a>
<a href="geometry/translations_3points_6units_3step_001.html" class=""><strong>Three-Step</strong> Translation of 3 vertices by up to 6 units.</a>
<a href="geometry/translations_4points_6units_3step_001.html" class=""><strong>Three-Step</strong> Translation of 4 vertices by up to 6 units.</a>
</div>
</li>
<li><p>Reflect on this: reflecting shapes over horizontal or vertical lines is actually quite straight-forward, especially if there is a grid involved. Start at one of the original points/vertices and measure the distance to the reflecting line. Note that you should measure perpendicularly or 90 degrees toward the line which is why it is easier with vertical or horizontal reflecting lines than with diagonal lines. Measure out 90 degrees on the other side of the reflecting line, the same distance of course, and make a point to represent the reflected vertex. Once you've done this for all of the vertices, you simply draw in the line segments and your reflected shape will be finished.</p></li>
<li><p>Reflecting can also be as simple as paper-folding. Fold the paper on the reflecting line and hold the paper up to the light. On a window is best because you will also have a surface on which to write. Only mark the vertices, don't try to draw the entire shape. Unfold the paper and use a pencil and ruler to draw the line segments between the vertices.</p></li>
<li><input type="checkbox" class="list-checkbox" id="transformations-16"><label for="transformations-16" class="wtitle">Reflections Worksheets</label>
<div class="desc">
<a href="geometry/reflections_y0x0_3vertices_001.html" class="">Reflection of 3 Vertices Over <i>x</i> = 0 and <i>y</i> = 0</a>
<a href="geometry/reflections_y0x0_4vertices_001.html" class="">Reflection of 4 Vertices Over <i>x</i> = 0 and <i>y</i> = 0</a>
<a href="geometry/reflections_y0x0_5vertices_001.html" class="">Reflection of 5 Vertices Over <i>x</i> = 0 and <i>y</i> = 0</a>
<a href="geometry/reflections_y4x4_3vertices_001.html" class="">Reflection of 3 Vertices Over Various Lines</a>
<a href="geometry/reflections_y4x4_4vertices_001.html" class="">Reflection of 4 Vertices Over Various Lines</a>
<a href="geometry/reflections_y4x4_5vertices_001.html" class="">Reflection of 5 Vertices Over Various Lines</a>
</div>
</li>
<li><input type="checkbox" class="list-checkbox" id="transformations-17"><label for="transformations-17" class="wtitle">Reflections Worksheets (Multi-Step)</label>
<div class="desc">
<a href="geometry/reflections_y4x4_3vertices_2step_001.html" class=""><strong>Two-Step</strong> Reflection of 3 Vertices Over Various Lines</a>
<a href="geometry/reflections_y4x4_4vertices_2step_001.html" class=""><strong>Two-Step</strong> Reflection of 4 Vertices Over Various Lines</a>
<a href="geometry/reflections_y4x4_3vertices_3step_001.html" class=""><strong>Three-Step</strong> Reflection of 3 Vertices Over Various Lines</a>
<a href="geometry/reflections_y4x4_4vertices_3step_001.html" class=""><strong>Three-Step</strong> Reflection of 4 Vertices Over Various Lines</a>
</div>
</li>
<li><p>Here's an idea on how to complete rotations without measuring. It works best on a grid and with 90 or 180 degree rotations. You will need a blank overhead projector sheet or other suitable clear plastic sheet and a pen that will work on the page. Non-permanent pens are best because the plastic sheet can be washed and reused. Place the sheet over top of the coordinate axes with the figure to be rotated. With the pen, make a small cross to show the <i>x</i> and <i>y</i> axes being as precise as possible. Also mark the vertices of the shape to be rotated. Using the plastic sheet, perform the rotation, lining up the cross again with the axes. Choose one vertex and mark it on the paper by holding the plastic sheet in place, but flipping it up enough to get a mark on the paper. Do this for the other vertices, then remove the plastic sheet and join the vertices with line segments using a ruler.</p></li>
<li><input type="checkbox" class="list-checkbox" id="transformations-18"><label for="transformations-18" class="wtitle">Rotations Worksheets</label>
<div class="desc">
<a href="geometry/rotations_origin_3vertices_startquadrant1_001.html" class="">Rotation of 3 Vertices around the <strong>Origin</strong> Starting in Quadrant I</a>
<a href="geometry/rotations_origin_4vertices_startquadrant1_001.html" class="">Rotation of 4 Vertices around the <strong>Origin</strong> Starting in Quadrant I</a>
<a href="geometry/rotations_origin_5vertices_startquadrant1_001.html" class="">Rotation of 5 Vertices around the <strong>Origin</strong> Starting in Quadrant I</a>
<a href="geometry/rotations_origin_3vertices_001.html" class="">Rotation of 3 Vertices around the <strong>Origin</strong></a>
<a href="geometry/rotations_origin_4vertices_001.html" class="">Rotation of 4 Vertices around the <strong>Origin</strong></a>
<a href="geometry/rotations_origin_5vertices_001.html" class="">Rotation of 5 Vertices around the <strong>Origin</strong></a>
<a href="geometry/rotations_anypoint_3vertices_001.html" class="">Rotation of 3 Vertices around <strong>Any Point</strong></a>
<a href="geometry/rotations_anypoint_4vertices_001.html" class="">Rotation of 4 Vertices around <strong>Any Point</strong></a>
<a href="geometry/rotations_anypoint_5vertices_001.html" class="">Rotation of 5 Vertices around <strong>Any Point</strong></a>
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<li><input type="checkbox" class="list-checkbox" id="transformations-19"><label for="transformations-19" class="wtitle">Rotations Worksheets (Multi-Step)</label>
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<a href="geometry/rotations_anypoint_3vertices_2steps_001.html" class="">Two-Step Rotations of 3 Vertices around <strong>Any Point</strong></a>
<a href="geometry/rotations_anypoint_4vertices_2steps_001.html" class="">Two-Step Rotations of 4 Vertices around <strong>Any Point</strong></a>
<a href="geometry/rotations_anypoint_5vertices_2steps_001.html" class="">Two-Step Rotations of 5 Vertices around <strong>Any Point</strong></a>
<a href="geometry/rotations_anypoint_3vertices_3steps_001.html" class="">Three-Step Rotations of 3 Vertices around <strong>Any Point</strong></a>
<a href="geometry/rotations_anypoint_4vertices_3steps_001.html" class="">Three-Step Rotations of 4 Vertices around<strong>Any Point</strong></a>
<a href="geometry/rotations_anypoint_5vertices_3steps_001.html" class="">Three-Step Rotations of 5 Vertices around <strong>Any Point</strong></a>
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<li><input type="checkbox" class="list-checkbox" id="transformations-20"><label for="transformations-20" class="wtitle">Dilations Worksheets</label>
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<a href="geometry/dilations_0center_3vertices_4scale_5point_001.html" class="">Dilations Using Center (0, 0)</a>
<a href="geometry/dilations_3center_3vertices_4scale_5point_001.html" class="">Dilations Using Various Centers</a>
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<li><input type="checkbox" class="list-checkbox" id="transformations-21"><label for="transformations-21" class="wtitle">Determining Scale Factors Worksheets</label>
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<a href="geometry/scale_factor_rectangles_whole_intervals_001.html" class="">Determine Scale Factors of Rectangles (Whole Numbers)</a>
<a href="geometry/scale_factor_rectangles_half_intervals_001.html" class="">Determine Scale Factors of Rectangles (0.5 Intervals)</a>
<a href="geometry/scale_factor_rectangles_tenth_intervals_001.html" class="">Determine Scale Factors of Rectangles (0.1 Intervals)</a>
<a href="geometry/scale_factor_triangles_whole_intervals_001.html" class="">Determine Scale Factors of Triangles (Whole Numbers)</a>
<a href="geometry/scale_factor_triangles_half_intervals_001.html" class="">Determine Scale Factors of Triangles (0.5 Intervals)</a>
<a href="geometry/scale_factor_triangles_tenth_intervals_001.html" class="">Determine Scale Factors of Triangles (0.1 Intervals)</a>
<a href="geometry/scale_factor_trirectangles_whole_intervals_001.html" class="">Determine Scale Factors of Rectangles and Triangles (Whole Numbers)</a>
<a href="https://math-drills.com/geometry/scale_factor_trirectangles_half_intervals_001.php" class="">Determine Scale Factors of Rectangles and Triangles (0.5 Intervals)</a>
<a href="https://math-drills.com/geometry/scale_factor_trirectangles_tenth_intervals_001.php" class="">Determine Scale Factors of Rectangles Triangles (0.1 Intervals)</a>
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<li><input type="checkbox" class="list-checkbox" id="transformations-22"><label for="transformations-22" class="wtitle">Mixed Transformations Worksheets (Multi-Step)</label>
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<a href="https://math-drills.com/geometry/two-step-transformations_001.php" class="">Two-Step Transformations</a>
<a href="https://math-drills.com/geometry/three-step-transformations_001.php" class="">Three-Step Transformations</a>
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</li>
</ul>
</div>
</div>
<div class="wscontainer bc01">
<div class="titlearea">
<h2 id="constructions">Constructions Worksheets</h2>
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<img src="https://math-drills.com/geometry/images/constructions_perpendicular_line_rotated_online_001_300.004.jpg" alt="" width="250" height="324" loading="lazy">
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<li><p>Constructions worksheets for constructing bisectors, perpendicular lines and triangle centers.</p></li>
<li><p>It is amazing what one can accomplish with a compass, a straight-edge and a pencil. In this section, students will do math like Euclid did over 2000 years ago. Not only will this be a lesson in history, but students will gain valuable skills that they can use in later math studies.</p></li>
<li><input type="checkbox" class="list-checkbox" id="constructions-23"><label for="constructions-23" class="wtitle">Constructing Midpoints And Bisectors On Line Segments And Angles</label>
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<a href="https://math-drills.com/geometry/constructions_midpoint_horizontal_001.php" class="">Midpoints on Horizontal Line Segments</a>
<a href="https://math-drills.com/geometry/constructions_perpendicular_bisector_horizontal_001.php" class="">Perpendicular Bisectors on Horizontal Line Segments</a>
<a href="https://math-drills.com/geometry/constructions_perpendicular_bisector_001.php" class="">Perpendicular Bisectors on Rotated Line Segments</a>
<a href="https://math-drills.com/geometry/constructions_angle_bisector_flat_001.php" class="">Angle Bisectors (Angles not Rotated)</a>
<a href="https://math-drills.com/geometry/constructions_angle_bisector_rotated_001.php" class="">Angle Bisectors (Angles Randomly Rotated)</a>
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<li><input type="checkbox" class="list-checkbox" id="constructions-24"><label for="constructions-24" class="wtitle">Constructing Perpendicular Lines</label>
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<a href="https://math-drills.com/geometry/constructions_perpendicular_line_horizontal_online_001.php" class="">Construct Perpendicular Lines Through Points on a Line Segment</a>
<a href="https://math-drills.com/geometry/constructions_perpendicular_line_horizontal_offline_001.php" class="">Construct Perpendicular Lines Through Points Not on Line Segment</a>
<a href="https://math-drills.com/geometry/constructions_perpendicular_line_rotated_online_001.php" class="">Construct Perpendicular Lines Through Points on Line Segment (Segments are randomly rotated)</a>
<a href="https://math-drills.com/geometry/constructions_perpendicular_line_rotated_offline_001.php" class="">Construct Perpendicular Lines Through Points Not on Line Segment (Segments are randomly rotated)</a>
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<li><input type="checkbox" class="list-checkbox" id="constructions-25"><label for="constructions-25" class="wtitle">Constructing Triangle Centers</label>
<div class="desc">
<a href="https://math-drills.com/geometry/constructions_triangle_centers_centroid_acute_001.php" class="">Centroids for Acute Triangles</a>
<a href="https://math-drills.com/geometry/constructions_triangle_centers_centroid_mixed_001.php" class="">Centroids for Mixed Acute and Obtuse Triangles</a>
<a href="https://math-drills.com/geometry/constructions_triangle_centers_orthocenter_acute_001.php" class="">Orthocenters for Acute Triangles</a>
<a href="https://math-drills.com/geometry/constructions_triangle_centers_orthocenter_mixed_001.php" class="">Orthocenters for Mixed Acute and Obtuse Triangles</a>
<a href="https://math-drills.com/geometry/constructions_triangle_centers_incenter_acute_001.php" class="">Incenters for Acute Triangles</a>
<a href="https://math-drills.com/geometry/constructions_triangle_centers_incenter_mixed_001.php" class="">Incenters for Mixed Acute and Obtuse Triangles</a>
<a href="https://math-drills.com/geometry/constructions_triangle_centers_circumcenter_acute_001.php" class="">Circumcenters for Acute Triangles</a>
<a href="https://math-drills.com/geometry/constructions_triangle_centers_circumcenter_mixed_001.php" class="">Circumcenters for Mixed Acute and Obtuse Triangles</a>
<a href="https://math-drills.com/geometry/constructions_triangle_centers_allcenters_acute_001.php" class="">All Centers for Acute Triangles</a>
<a href="https://math-drills.com/geometry/constructions_triangle_centers_allcenters_mixed_001.php" class="">All Centers for Mixed Acute and Obtuse Triangles</a>
</div>
</li>
</ul>
</div>
</div>
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<div class="titlearea">
<h2 id="three-dimensional-geometry">Three-Dimensional Geometry</h2>
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<div class="imagearea">
<img src="https://math-drills.com/geometry/images/geo_ccstructuresbuild_001_300.004.jpg" alt="" width="250" height="324" loading="lazy">
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<div class="worksheetsarea">
<ul class="list">
<li><p>Three-dimensional geometry worksheets that are based on connecting cubes and worksheets for classifying three-dimensional figures.</p></li>
<li><p>Connecting cubes can be a powerful tool for developing spatial sense in students. The first two worksheets below are difficult to do even for adults, but with a little practice, students will be creating structures much more complex than the ones below. Use isometric grid paper and square graph paper or dot paper to help students create three-dimensional sketches of connecting cubes and side views of structures.</p></li>
<li><input type="checkbox" class="list-checkbox" id="three-dimensional-geometry-26"><label for="three-dimensional-geometry-26" class="wtitle">Connecting Cube Structures</label>
<div class="desc">
<a href="https://math-drills.com/geometry/geo_ccstructures_side_views_001.php" class="">Side Views of Connecting Cube Structures</a>
<a href="https://math-drills.com/geometry/geo_ccstructuresbuild_001.php" class="">Build Connecting Cube Structures</a>
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</li>
<li><input type="checkbox" class="list-checkbox" id="three-dimensional-geometry-27"><label for="three-dimensional-geometry-27" class="wtitle">Classifying Three-Dimensional Figures</label>
<div class="desc">
<a href="https://math-drills.com/geometry/geometry_classify_prisms_001.php" class="">Classify Prisms</a>
<a href="https://math-drills.com/geometry/geometry_classify_pyramids_001.php" class="">Classify Pyramids</a>
<a href="https://math-drills.com/geometry/geometry_classify_prisms_pyramids_001.php" class="">Classify Prisms and Pyramids</a>
</div>
</li>
<li><p>This section includes a number of nets that students can use to build the associated 3D solids. All of the Platonic solids and many of the Archimedean solids are included. A pair of scissors, a little tape and some dexterity are all that are needed. For something a little more substantial, copy or print the nets onto cardstock first. You may also want to check your print settings to make sure you print in "actual size" rather than fitting to the page, so there is no distortion.</p></li>
<li><input type="checkbox" class="list-checkbox" id="three-dimensional-geometry-28"><label for="three-dimensional-geometry-28" class="wtitle">Nets of Three-Dimensional Figures</label>
<div class="desc">
<a href="https://math-drills.com/geometry/net_platonic_archimedean_solids.php" class="">Nets of Platonic and Archimedean Solids</a>
<a href="https://math-drills.com/geometry/net_platonic_solids.php" class="">Nets of All Platonic Solids</a>
<a href="https://math-drills.com/geometry/net_archimedean_solids.php" class="">Nets of Some Archimedean Solids</a>
<a href="https://math-drills.com/geometry/net_tetrahedron.php" class="">Net of a Tetrahedron</a>
<a href="https://math-drills.com/geometry/net_cube.php" class="">Net of a Cube</a>
<a href="https://math-drills.com/geometry/net_octahedron.php" class="">Net of an Octahedron</a>
<a href="https://math-drills.com/geometry/net_dodecahedron1.php" class="">Net of a Dodecahedron (Version 1)</a>
<a href="https://math-drills.com/geometry/net_dodecahedron2.php" class="">Net of a Dodecahedron (Version 2)</a>
<a href="https://math-drills.com/geometry/net_icosahedron.php" class="">Net of an Icosahedron</a>
<a href="https://math-drills.com/geometry/net_truncated_tetrahedron.php" class="">Net of a Truncated Tetrahedron</a>
<a href="https://math-drills.com/geometry/net_cuboctahedron.php" class="">Net of a Cuboctahedron</a>
<a href="https://math-drills.com/geometry/net_truncated_cube.php" class="">Net of a Truncated Cube</a>
<a href="https://math-drills.com/geometry/net_truncated_octahedron.php" class="">Net of a Truncated Octahedron</a>
<a href="https://math-drills.com/geometry/net_rhombicuboctahedron.php" class="">Net of a Rhombicuboctahedron</a>
<a href="https://math-drills.com/geometry/net_truncated_cuboctahedron.php" class="">Net of a Truncated Cuboctahedron</a>
<a href="https://math-drills.com/geometry/net_snub_cube.php" class="">Net of a Snub Cube</a>
<a href="https://math-drills.com/geometry/net_icosidodecahedron.php" class="">Net of an Icosidodecahedron</a>
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</li>
</ul>
</div>
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