Virginia Department of Education
Congruent Triangles
Is this enough to show the two triangles are congruent? Small groups work through different combinations of constructing triangles from congruent parts to determine which combinations create only congruent triangles. Participants use the...
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...
Shodor Education Foundation
Squaring the Triangle
Teach budding mathematicians how to square a triangle with an interactive that shows a graphical proof of the Pythagorean Theorem. Pupils alter the lengths of the legs using sliders. Using the inputted lengths, the applet displays the...
Chapman University
A Pythagorean-Style Proof of the Sine Sum-of-Angles Formula
This well organized poster shows a step-by-step algebraic proof and related graphic. Understanding how formulas were derived, connects learners to the idea that the study of mathematics is continuous and cumulative. Learners will also...
Curated OER
Inductive vs. Deductive Proof
Twelfth graders differentiate between inductive and deductive proofs. In this differentiating between inductive and deductive proofs lesson, 12th graders compare strengths and weaknesses of each type of proof. Students discuss an...
Curated OER
From Hypothesis to Conclusion...Reading Maps to Understand Proofs
Tenth graders explore the concept of proof. In this proof lesson, 10th graders work in groups to collectively write proofs for directions to places on a map. Students give directions to specific places in big cities such as from the New...
Curated OER
Geometric Proof and Angles
In this geometry instructional activity, 10th graders write two-column and paragraph proofs to prove angle pair relationships. The one page instructional activity contains five problems. Answers are not included.
Curated OER
The Proof Is in the Picture
Students select a geometric figure and find an example of the figure in their surroundings. They photograph the figure and write a proof to accompany it. They match photos to proofs.
Curated OER
Using Proof in Algebra
In this using proofs in algebra activity, 10th graders solve 2 proofs by applying the many rules from algebra for the Properties of Equality for real numbers. They name the property that justifies each statement as seen in the...
Curated OER
Identify Similar Triangles With Proofs
In this similar triangle activity, students write a two-column proof to explain why determined triangles are similar. Given some line lengths and angle measurements, students use proofs to identify the ratio of specified angles. This...
Curated OER
Discovering Math: Concepts in Geometry
Middle and high schoolers explore the concept of proving the Pythagorean Theorem. They research proofs of the Pythagorean Theorem. Pupils create posters of proofs, and research Greek mathematicians.
Mathematics Vision Project
Module 6: Congruence, Construction, and Proof
Trace the links between a variety of math concepts in this far-reaching unit. Ideas that seem very different on the outset (like the distance formula and rigid transformations) come together in very natural and logical ways. This unit...
EngageNY
Base Angles of Isosceles Triangles
Build confidence in proofs by proving a known property. Pupils explore two approaches to proving base angles of isosceles triangles are congruent: transformations and SAS. They then apply their understanding of the proof to more complex...
EngageNY
The Graph of a Linear Equation in Two Variables Is a Line
Show your class that linear equations produce graphs of lines. The 20th segment in a unit of 33 provides proof that the graph of a two-variable linear equation is a line. Scholars graph linear equations using two points, either from...
Flipped Math
Proving Lines Parallel
Show it can all be proved. Scholars learn the converses of the properties of parallel lines. Using the converses, pupils determine which lines are parallel based on angle measurements and practice using a flow proof to show that two...
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...
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
Quiz: Direct Euclidean Proofs
In this Euclidean proof worksheet, students observe models and read given proofs. Students determine conclusions based upon the given information. This one-page worksheet contains ten Euclidean proof problems.
Curated OER
Algebraic Proofs for Repeated Digits
In this proof worksheet, students write two proofs for why they get repeated digits when following a series of math operations. The solutions are provided.
Curated OER
Proofs
In this proofs learning exercise, 10th graders solve and graph 8 different equations. First, they prove that each triangle is either congruent or similar. Then, students use the concept of corresponding parts of congruent triangles to...
Curated OER
Pre-Proof Warm-Ups
For this pre-proofs worksheet, 10th graders solve and complete 10 different problems that include various proofs and their definitions. They use the diagram shown and the given information to write the direct conclusion for each case....
Curated OER
Geometry Proofs
In this geometry proofs worksheet, 10th graders solve and complete 6 different problems that include various proofs. First, they prove a triangle has equivalent angles as given. Then, students prove two angles supplementary as described.
Curated OER
Proofs in Coordinate Geometry
In this coordinate geometry activity, students identify the lengths of a quadrilateral and find the slope of a line. They use proofs to identify the characteristics of given quadrilaterals. This one-page activity contains ten problems.
Curated OER
Proofs: Solving Equations
In this proofs worksheet, high schoolers solve 4 short answer problems. Students identify the correct reason for each step in solving each multi-step equation.
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