Geometry Worksheets

Welcome to the geometry worksheets page at Math-Drills.com where we believe that there is nothing wrong with being square! This page includes Geometry Worksheets on angles, coordinate geometry, triangles, quadrilaterals, transformations and three-dimensional geometry worksheets.

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.

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.

Most Popular Geometry Worksheets this Week

Plotting Coordinate Points

Lines and Angles

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In this section, there are worksheets for two of the basic concepts of geometry: lines and angles.

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.

  • Identifying Lines, Line Segments and Rays Identify Lines, Segments and Rays

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.

  • Identifying Angle Types Worksheets Identifying Acute and Obtuse Angles Identifying Acute and Obtuse Angles (No Angle Marks) Identifying Acute, Obtuse and Right Angles Identifying Acute, Obtuse and Right Angles (No Angle Marks) Identifying Acute, Obtuse, Right and Straight Angles Identifying Acute, Obtuse, Right and Straight Angles (No Angle Marks) Identifying Acute, Obtuse, Right, Straight and Reflex Angles Identifying Acute, Obtuse, Right, Straight, Reflex and Complete/Full Angles

There are several angle relationships of which students should be aware. Complementary angles are two angles that together form a 90 degree angle; supplementary angles are two angles that together form a 180 degree angle; and explementary angles are two angles that together form a 360 degree angle. Vertical angles 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.

  • Angle Relationships Worksheets Complementary Angles Complementary Angles (Diagrams Rotated) Supplementary Angles Supplementary Angles (Diagrams Rotated) Mixed Complementary and Supplementary Angles Questions (Diagrams Rotated) Explementary Angles Explementary Angles (Diagrams Rotated) Mixed Adjacent Angles Questions (Diagrams Rotated) Vertical/Opposite Angles Vertical/Opposite Angles (Diagrams Rotated) Mixed Angle Relationships Questions(Diagrams Rotated)
  • Angles of Transversals Intersecting Parallel Lines Interior Alternate Angles Exterior Alternate Angles Alternate Angles Corresponding Angles Co-Interior Angles Transversals

Measuring angles worksheets, can be found on the Measurement Page

Triangles, Quadrilaterals and Other Shapes

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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.

  • Shape Sets Quadrilaterals Set Tangrams
  • Identifying Regular Polygons Identifying Regular Shapes from Triangles to Octagons

Worksheets for classifying triangles by side and angle properties and for working with Pythagorean theorem.

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.

  • Classifying Triangles Worksheets Classifying Triangles by Side Properties Classifying Triangles by Angle Properties Classifying Triangles by Side and Angle Properties Classifying Triangles by Side Properties (No Marks) Classifying Triangles by Angle Properties (No Marks) Classifying Triangles by Side and Angle Properties (No Marks)

A cathetus (plural catheti) refers to a side of a right-angle triangle other than the hypotenuse.

  • Calculating Triangle Dimensions Using Pythagorean Theorem Calculate the Hypotenuse Using Pythagorean Theorem (No Rotation) Calculate the Hypotenuse Using Pythagorean Theorem Calculate a Cathetus Using Pythagorean Theorem (No Rotation) Calculate a Cathetus Using Pythagorean Theorem Calculate any Side Using Pythagorean Theorem (No Rotation) Calculate any Side Using Pythagorean Theorem

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.

  • Calculating Angles and Sides Using Trigonometric Ratios Calculating Angles Using the Sine Ratio Calculating Sides Using the Sine Ratio Calculating Angles and Sides Using the Sine Ratio Calculating Angles Using the Cosine Ratio Calculating Sides Using the Cosine Ratio Calculating Angles and Sides Using the Cosine Ratio Calculating Angles Using the Tangent Ratio Calculating Sides Using the Tangent Ratio Calculating Angles and Sides Using the Tangent Ratio Calculating Angles Using Trigonometric Ratios Calculating Sides Using Trigonometric Ratios Calculating Angles and Sides Using Trigonometric Ratios

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.

  • Classifying Quadrilaterals Classifying Simple Quadrilaterals Classifying All Quadrilaterals Classifying All Quadrilaterals (+ Rotation)

Coordinate Plane Worksheets

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Coordinate point geometry worksheets to help students learn about the Cartesian plane.

  • Plotting Random Coordinate Points Plotting Coordinate Points in All Quadrants Plotting Coordinate Points in Positive x Quadrants Plotting Coordinate Points in Positive y Quadrants

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.

  • Cartesian Art Cartesian Art Maple Leaf
  • Coordinate Plane Distance and Area Calculating Pythagorean Distances of Coordinate Points Calculating Perimeter and Area of Triangles on Coordinate Planes Calculating Perimeter and Area of Quadrilaterals on Coordinate Planes Calculating Perimeter and Area of Triangles and Quadrilaterals on Coordinate Planes

Transformations Worksheets

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Transformations worksheets for translations, reflections, rotations and dilations practice.

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.

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.

  • Translations Worksheets Translation of 3 vertices by up to 3 units. Translation of 3 vertices by up to 6 units. Translation of 3 vertices by up to 25 units. Translation of 4 vertices by up to 6 units. Translation of 5 vertices by up to 6 units.
  • Translations Worksheets (Multi-Step) Two-Step Translation of 3 vertices by up to 6 units. Two-Step Translation of 4 vertices by up to 6 units. Three-Step Translation of 3 vertices by up to 6 units. Three-Step Translation of 4 vertices by up to 6 units.

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.

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.

  • Reflections Worksheets Reflection of 3 Vertices Over x = 0 and y = 0 Reflection of 4 Vertices Over x = 0 and y = 0 Reflection of 5 Vertices Over x = 0 and y = 0 Reflection of 3 Vertices Over Various Lines Reflection of 4 Vertices Over Various Lines Reflection of 5 Vertices Over Various Lines
  • Reflections Worksheets (Multi-Step) Two-Step Reflection of 3 Vertices Over Various Lines Two-Step Reflection of 4 Vertices Over Various Lines Three-Step Reflection of 3 Vertices Over Various Lines Three-Step Reflection of 4 Vertices Over Various Lines

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 x and y 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.

  • Rotations Worksheets Rotation of 3 Vertices around the Origin Starting in Quadrant I Rotation of 4 Vertices around the Origin Starting in Quadrant I Rotation of 5 Vertices around the Origin Starting in Quadrant I Rotation of 3 Vertices around the Origin Rotation of 4 Vertices around the Origin Rotation of 5 Vertices around the Origin Rotation of 3 Vertices around Any Point Rotation of 4 Vertices around Any Point Rotation of 5 Vertices around Any Point
  • Rotations Worksheets (Multi-Step) Two-Step Rotations of 3 Vertices around Any Point Two-Step Rotations of 4 Vertices around Any Point Two-Step Rotations of 5 Vertices around Any Point Three-Step Rotations of 3 Vertices around Any Point Three-Step Rotations of 4 Vertices around Any Point Three-Step Rotations of 5 Vertices around Any Point
  • Dilations Worksheets Dilations Using Center (0, 0) Dilations Using Various Centers
  • Determining Scale Factors Worksheets Determine Scale Factors of Rectangles (Whole Numbers) Determine Scale Factors of Rectangles (0.5 Intervals) Determine Scale Factors of Rectangles (0.1 Intervals) Determine Scale Factors of Triangles (Whole Numbers) Determine Scale Factors of Triangles (0.5 Intervals) Determine Scale Factors of Triangles (0.1 Intervals) Determine Scale Factors of Rectangles and Triangles (Whole Numbers) Determine Scale Factors of Rectangles and Triangles (0.5 Intervals) Determine Scale Factors of Rectangles Triangles (0.1 Intervals)
  • Mixed Transformations Worksheets (Multi-Step) Two-Step Transformations Three-Step Transformations

Constructions Worksheets

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Constructions worksheets for constructing bisectors, perpendicular lines and triangle centers.

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.

  • Constructing Midpoints And Bisectors On Line Segments And Angles Midpoints on Horizontal Line Segments Perpendicular Bisectors on Horizontal Line Segments Perpendicular Bisectors on Rotated Line Segments Angle Bisectors (Angles not Rotated) Angle Bisectors (Angles Randomly Rotated)
  • Constructing Perpendicular Lines Construct Perpendicular Lines Through Points on a Line Segment Construct Perpendicular Lines Through Points Not on Line Segment Construct Perpendicular Lines Through Points on Line Segment (Segments are randomly rotated) Construct Perpendicular Lines Through Points Not on Line Segment (Segments are randomly rotated)
  • Constructing Triangle Centers Centroids for Acute Triangles Centroids for Mixed Acute and Obtuse Triangles Orthocenters for Acute Triangles Orthocenters for Mixed Acute and Obtuse Triangles Incenters for Acute Triangles Incenters for Mixed Acute and Obtuse Triangles Circumcenters for Acute Triangles Circumcenters for Mixed Acute and Obtuse Triangles All Centers for Acute Triangles All Centers for Mixed Acute and Obtuse Triangles

Three-Dimensional Geometry

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Three-dimensional geometry worksheets that are based on connecting cubes and worksheets for classifying three-dimensional figures.

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.

  • Connecting Cube Structures Side Views of Connecting Cube Structures Build Connecting Cube Structures
  • Classifying Three-Dimensional Figures Classify Prisms Classify Pyramids Classify Prisms and Pyramids

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.

  • Nets of Three-Dimensional Figures Nets of Platonic and Archimedean Solids Nets of All Platonic Solids Nets of Some Archimedean Solids Net of a Tetrahedron Net of a Cube Net of an Octahedron Net of a Dodecahedron (Version 1) Net of a Dodecahedron (Version 2) Net of an Icosahedron Net of a Truncated Tetrahedron Net of a Cuboctahedron Net of a Truncated Cube Net of a Truncated Octahedron Net of a Rhombicuboctahedron Net of a Truncated Cuboctahedron Net of a Snub Cube Net of an Icosidodecahedron

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Geometry Worksheets(pdf)

Free worksheets with answer keys.

Enjoy these free sheets. Each one has model problems worked out step by step, practice problems, as well as challenge questions at the sheets end. Plus each one comes with an answer key.

  • Graphic Organizer on All Formulas
  • Interior Angles of Polygons
  • Exterior Angles of Polygons
  • Similar Polygons
  • Area of Triangle
  • Interior Angles of Triangle

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Free math worksheets for Geometry. Every worksheet pdf contains 10 different assignments. To open and print the worksheets you will need to have a Adobe Acrobat Reader installed.

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Geometry Resources

Below you will find links to program resources organized by module and topic, including Family Guides, Assignment pages, and more!

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Module 1: reasoning with shapes.

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Module 2: Establishing Congruence

Module 3: inverting functions, module 4: connecting geometric and algebraic descriptions, module 5: making informed decisions, other resources, math glossary.

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  1. Free Printable Math Worksheets for Geometry

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  2. Geometry Worksheets

    This page includes Geometry Worksheets on angles, coordinate geometry, triangles, quadrilaterals, transformations and three-dimensional geometry worksheets. Get out those rulers, protractors and compasses because we've got some great worksheets for geometry!

  3. Free Math Worksheets (pdfs) with answer keys on Algebra I, Geometry

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  4. Geometry Worksheets (pdf) with answer keys

    Geometry Worksheets (pdf) Free worksheets with answer keys Mathworksheetsgo.com is now a part of Mathwarehouse.com. All of your worksheets are now here on Mathwarehouse.com. Please update your bookmarks! Enjoy these free sheets. Each one has model problems worked out step by step, practice problems, as well as challenge questions at the sheets end.

  5. PDF Geometry (Part 1) Lines and angles

    Angles that add up to 90°. Supplementary angles. Angles that add up to 180°. E.g. the complement of 48° is 42°. E.g. the supplement of 130° is 50°. Adjacent angles Adjacent angels on a straight line adds up to 180° ∴ + = 180°. Angles that have a common vertex and a common arm → and are adjacent angles. Perpendicular lines.

  6. PDF Date Block # Chapter 1& 2: Introduction to Geometry Assignment

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  8. Geometry

    Every worksheet pdf contains 10 different assignments. To open and print the worksheets you will need to have a Adobe Acrobat Reader installed. Circles (0) Congruent Triangles (0) Constructions (0) Parallel Lines and the Coordinate Plane (0) Properties of Triangles (0) Quadrilaterals and Polygons (0) Display Num Geometry Circles Segment measures

  9. PDF 6-Area of Regular Polygons

    10) octagon apothem = 14.1 side = 11.7. 1602.3. 659.88. Use what you know about special right triangles to find the area of each regular polygon. Leave your answer in simplest form. 11) 243 3. 96 3. 25 3.

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  11. PDF Introduction to Geometry Worksheet I

    Introduction to Geometry Worksheet I 1. Given ! "LOM 83 and LON! "142 , find the measure of MON. M 2. Given ! "LOM 42 and LON! "93 , find the measure of MON. Find the measure of x. 3. 4. Given LON is a right angle, find the measure of x. 5. 6. 5x O 7. 8. x 34 x 74 88 158 O N L O N M L x N M L 2x x O N M L x O L M N x + 31 x O N M L x+14

  12. PDF Geometry: Surface Area and Volume (Advanced)

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  13. PDF 4-SSS, SAS, ASA, and AAS Congruence

    Kuta Software - Infinite Geometry Name_____ SSS, SAS, ASA, and AAS Congruence Date_____ Period____ State if the two triangles are congruent. If they are, state how you know. 1) Not congruent 2) ASA 3) SSS 4) ASA 5) Not congruent 6) ASA 7) Not congruent 8) SSS 9) SAS 10) SSS-1-©3 Y2v0V1n1 Y AKFuBt sal MSio 4fWtYwza XrWed 0LBLjC S.N W uA 0lglq ...

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    Introduction to proofs: Identifying geometry theorems and postulates ANSWERS C congruent ? Explain using geometry concepts and theorems: 1) Why is the triangle isosceles? PR and PQ are radii of the circle. Therefore, they have the same length. A triangle with 2 sides of the same length is isosceles. 2) Why is an altitude? AB = AB (reflexive ...

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    author's extensive experience in professional mathematics in a business setting and in math tutoring. Contains free downloadable handbooks, PC Apps, sample tests, and more. Broken Arrow, Oklahoma Standard Geometry Test - A standardized Geometry test released by the state of Oklahoma. A good way to test your knowledge. Version 4.2 Page 5 of 137

  17. PDF Circles and Geometry

    Circles and Geometry: Notes and Examples Example: BC=5 CD=8 Find the length of chord AB Note: is tangent to circle O "Secant - Tangent Theorem" : When a secant and a tangent share an endpoint outside the circle, the length of the tangent squared equals the product of the secant and the extemal segment. (CD) = 64 = + 25 39 = 39 so, chord AB — 7.8

  18. PDF Geometry Summer Assignment

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  19. Honors Geometry

    Honors Geometry (Period 2) Honors Geometry is a class designed for 9th grade students who have successfully passed Algebra I in middle school and for 10th/11th grade students that have shown above average skills in Algebra 1. Honors Geometry is a course where students will work on projects and real world applications in order to understand how ...

  20. PDF Geometry (GEOM) 1A Syllabus

    Throughout this course, you will be encouraged to use the four-step problem-solving plan that is part of the mathematics curriculum. The four-step problem-solving plan consists of the following steps: Analyze Information, Formulate a Plan, Solve, and. Justify and Evaluate. This will give you a simple, yet effective, framework for organizing ...

  21. PDF Proofs Using Coordinate Geometry Assignment

    Name: _____ Period: _____ Date: _____ Proofs Using Coordinate Geometry Assignment

  22. 6.05 geometry assignment.pdf

    6.05 Geometry Assignment Calculation 1: Base Area Object 1 : Shoebox Object 2: Coconut Cream Can 3D shape: Rectangular Prism 3D shape: Cylinder Dimensions: Width: 7 inches Lenght: 12 inches Height: 4 inches Dimensions: Height: 4.5 inches Diameter: 3 inches Base of Object 1 : Rectangle Base of Object 2: Circle Formula for Area: A= L x W Formula f...

  23. Geometry Resources

    Module 1 Module 2 Module 3 Module 4 Module 5 Need help with an assignment? Get real-time hints to guide students through assignments with LiveHint, our new chatbot assistant that is accessible on any device. Check it out RESOURCES BY TOPIC Module 1: Reasoning with Shapes Topic 1 Family Guides Assignment Downloads: Lesson 1 Lesson 2 Lesson 3