Geometry (10th Grade) Math Worksheets, Lessons and Tests (Free PDF)
These geometry worksheets follow the Common Core State Standards chapter by chapter: each chapter has a lesson, a worksheet of at least 20 worksheet problems with solutions, a timed test with its answer key and an online quiz, all with a free PDF.
Key takeaway: High school Geometry studies rigid transformations and congruence, proofs about lines, angles, triangles and parallelograms, constructions, dilations and similarity, right triangle trigonometry, the Laws of Sines and Cosines, circles, coordinate geometry, and area and volume in modeling problems.
Geometry worksheets: all chapters
1. Points, Lines, Segments and Angles
Understand points, lines and planes · Find the length and midpoint of a segment · Understand an angle and how do angles add · Solve a segment or angle problem with a variable
2. Translations, Reflections and Rotations
Understand a transformation · Combine transformations
3. Symmetry of Polygons and Rigid Motions
Understand line symmetry · Understand rotational symmetry · Find the symmetries of a polygon
4. Congruent Triangles and Rigid Motions
Two triangles are congruent when a sequence of rigid motions maps one onto the other, so all corresponding sides and angles are equal.
5. Parallel Lines and Transversals
Understand vertical angles and linear pairs · Understand a perpendicular bisector · Find an unknown angle
6. Theorems About Triangles
Understand the triangle angle sum theorem · Understand the exterior angle theorem · Understand a midsegment · Understand medians and the centroid
7. Parallelograms and Quadrilaterals
Understand a parallelogram and what are its properties · Find missing measures in a quadrilateral
8. Geometric Constructions
Construct a perpendicular bisector · Bisect an angle · Construct an equilateral triangle, a square and a regular hexagon
9. Dilations and Similarity
Understand a dilation · Solve a similarity problem
10. Similar Triangle Theorems
Show triangles are similar · Measure something you cannot reach
11. Right Triangle Trigonometry
Understand the trigonometric ratios · Solve for a side or an angle · Understand angles of elevation and depression
12. Law of Sines and Law of Cosines
Find the area of a triangle with two sides and the included angle · Understand the Law of Sines · Understand the Law of Cosines · Solve a non-right triangle
13. Circles: Angles, Chords and Tangents
Understand central and inscribed angles · Understand true about an inscribed quadrilateral · Understand the properties of tangents · Solve a circle angle problem
14. Arc Length and Sector Area
Find arc length · Find the area of a sector · Understand a radian · Solve an arc or sector problem
15. Coordinate Geometry and Proofs
Write the equation of a parallel or perpendicular line · Divide a segment in a given ratio · Find lengths, perimeter and area from coordinates · Prove a fact with coordinates
16. Equations of Circles and Parabolas
The graph of (x – h) squared + (y – k) squared = r squared is a circle with center (h, k) and radius r, because the equation says every point is r units from the center.
17. Area, Volume and Dissection Arguments
Understand the circle formulas · Find the volume of a prism or a cylinder · Understand Cavalieri's principle · Find the volume of a pyramid or a cone
18. Cross Sections and Solids of Revolution
Understand a cross section · Understand the cross sections of a cylinder · Understand a solid of revolution
What students learn in Geometry
High school Geometry usually follows Algebra 1. It teaches students to prove statements about figures with logical reasoning, not only to compute measures.
Students study transformations, congruent and similar triangles, right triangle trigonometry, circles, coordinate geometry, and area and volume. In addition, the course strengthens algebra, because many problems end with an equation to solve.
- Congruence and proofs: transformations, triangle congruence criteria, and two-column proofs.
- Similarity and trigonometry: similar triangles, sine, cosine, tangent, and special right triangles.
- Circles: arcs, angles, chords, tangents, and equations of circles.
- Coordinate geometry and measurement: distance, midpoint, slope proofs, area, and volume.
A year plan with these geometry worksheets
Begin with tools and transformations, then move to congruence and proofs. Next, similarity leads naturally to trigonometry. After that, cover circles and coordinate geometry. Finally, end with area and volume formulas, which tie the course together.
How to use these geometry worksheets
Pick a chapter, read its one-page lesson, then solve the worksheet on paper and check every answer with the solutions page. Take the ten-question quiz to see what is still unclear, and finish with the timed test. Every page can be printed from its PDF button, and the quick practice at the bottom of each page gives ten new questions at every visit.
Geometry math: common questions
What grade is Geometry?
Geometry is usually taken in 10th grade, between Algebra 1 and Algebra 2.
Does Geometry include proofs?
Yes. Students prove theorems about angles, triangles and parallelograms using definitions, postulates and two-column or paragraph proofs.
Is trigonometry part of Geometry?
Right triangle trigonometry (sine, cosine, tangent) and the Laws of Sines and Cosines are part of the Common Core Geometry course.
Are there Geometry worksheets with answers?
Yes. Every chapter has at least 20 worksheet problems with step-by-step solutions and a free PDF.
How do you write a geometry proof?
List what is given, mark it on the figure, and state what you must prove. Then, write each statement with a reason: a definition, a postulate or a theorem. Finally, end with the statement you had to prove.
Is Geometry easier than Algebra 1?
It is different. Geometry relies more on visual reasoning and proofs, while Algebra 1 relies on symbolic manipulation. Some students who struggle in algebra do better in geometry, and the reverse is also true.