Illustrative Mathematics
Are They Similar?
Learners separate things that just appear similar from those that are actually similar. A diagram of triangles is given, and then a variety of geometric characteristics changed and the similarity of the triangles analyzed. Because the...
Illustrative Mathematics
Similar Triangles
Proving triangles are similar is often an exercise in applying one of the many theorems young geometers memorize, like the AA similarity criteria. But proving that the criteria themselves are valid from basic principles is a great...
Illustrative Mathematics
Shortest Line Segment from a Point P to a Line L
One of the hardest skills for many young geometers to grasp is to move beyond just declaring obvious things true, and really returning to fundamental principles for proof. This brief exercise stretches those proving muscles as the class...
Geometry Accelerated
Accelerated Geometry Review Sheet
Your geometry learners use their knowledge of various geometric concepts to write proofs. Starting with givens containing parallel line segments with transversals and triangles and quadrilaterals, and the mid-point and distance formulas;...
West Contra Costa Unified School District
The Parallelogram Law
Use your pupils' sense of curiosity to explore the Parallelogram Law. Here is an activity that outlines a complete lesson from beginning to end, allowing pupils to follow a conjecture through to the proof stage.
Curated OER
Proving Quadrilateral Properties
Working backwards can sometimes help you see a path to solving a problem. In this chapter, properites of quadrilaterials are proven by looking at flowcharts and working the probem backwards. Worked through examples are given, along with...
Curated OER
Geometry: Properties of Triangles
In this properties of triangles worksheet, students use their knowledge of triangles to find determine angle measurement. They use geometric theorems to prove equal angles. This three-page worksheet contains 15 multi-step geometry...
Curated OER
Using Properties Homework
In this geometry worksheet, 10th graders determine the property of the real number system that justifies each given statement and complete a two column proof in which they justifying the steps for solving an equation. The one page...
Curated OER
Geometric Proof and Angles
In this geometry activity, 10th graders write two-column and paragraph proofs to prove angle pair relationships. The one page activity contains five problems. Answers are not included.
Curated OER
Proofs Chapter 2: Geometry
In this geometry instructional activity, students look at given pictures and prove congruent lines and angles. This three-page instructional activity contains nine multi-step problems.
Math Worksheets Center
Congruent Triangle Proofs Quiz
A congruent triangles quiz challenges teenage mathematicians to complete a pair of geometric proofs. Each problem includes a picture of the triangles in question, a given set of information, and the five steps needed to finish the proof....
Curated OER
Proving Triangles Congruent
In this proving triangles congruent worksheet, 10th graders solve 4 different proofs for congruent triangles. First, they mark all congruent parts on each figure, then complete the prove statement and identify the postulate that can be...
Curated OER
Right Triangles
In this right triangles worksheet, 10th graders solve 5 problems that relate to different right triangles. First, they find the values of x and y so that each triangle is congruent to the other. Then, students write a two-column proof...
Curated OER
Parallelograms
In this parallelograms worksheet, 10th graders solve 8 different types of problems related to measuring various parallelograms. First, they use the figure, a parallelogram, illustrated at the top to solve each problem. Then, students...
Curated OER
Identifying Similar Triangles
In this identifying similar triangles worksheet, 10th graders solve 5 different proofs related to similar triangles. First, they identify the similar triangles in each figure and explain why they are similar, using the information to...
Curated OER
Verifying Segment Relationships
In this verifying segment relationships worksheet, 10th graders solve two proofs by following the same format used in algebra. They complete each of two proofs by naming the property that justifies each statement given. Students also...
Curated OER
Verifying Angle Relationships
In this angle relationships instructional activity, 10th graders solve 8 various problems related to verifying angle relationships. First, they complete each statement if the measure of specific angles are equal to 43 and 56. Then,...
Curated OER
Verifying Segment Relationships
In this verifying segment relationships worksheet, 10th graders solve 3 different proofs by verifying the segment relationship in each. They complete each proof given a specific statements supporting the statement with reasons. Then,...
Oswego City School District
Regents Exam Prep Center: Writing a Proof: Direct Euclidean Proofs
This site is a look into the world of geometric proofs. You'll learn what a proof is and about the different types of proofs. Try the practice page to check your understanding. Teachers can check out the teacher resources for lesson and...
OER Commons
Oer Commons: Mars: Proving the Pythagorean Theorem
This lesson is intended to help you assess how well learners are able to produce and evaluate geometrical proofs. PowerPoint slides are included with the lesson.
Science Education Resource Center at Carleton College
Serc: Pythagorean Theorem Investigations
In this activity, learners will gain an understanding of the Pythagorean theorem and will recognize the variety of ways in which theorems can be proved algebraically, geometrically and visually.
Other
Math Court: A Game of Proving Things
This site contains a game to help students better learn how to write proofs. The game has several different levels. The game can be played online or cards and board may be printed and used in the classroom.
Dartmouth College
Dartmouth College: The Different Styles of Euclid and Copernicus
A history of the differences between Euclid's and Copernicus's methods of proving geometric ideas.
University of British Columbia
University of British Columbia: Proof of the Pythagorean Theorem
A geometric model that proves the Pythagorean Theorem in a step-by-step diagram that students can advance at their own pace. Requires Java.