Proofs are usually an intimidating assignment. An engaging lesson focused on geometric proofs may reduce the anxiety! Pupils choose between several triangle proofs to complete and work on completing them. The...

Geometric figures are perfect to use for proofs. Scholars prove conjectures about whether given points lie on a triangle and about midpoints. They use a provided dialogue among fictional students to frame their responses.

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...

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...

Given a pair of parallel lines and a triangle in between, geometers prove that the sum of the interior angles is 180 degrees. This quick quest can be used as a pop quiz or exit ticket for your geometry class.

A deceptively simple question setup leads to a number of attack methods and a surprisingly sophisticated solution set in this open-ended problem. Young geometers of different strengths can go about defining the solutions graphically,...

Without ever using the actual term, this exercise has the learner develop the key properties of the midsegment of a triangle. This task leads the class to discover a proof of similar triangles using the properties of parallel...

While it may seem incredibly obvious to the geometry student that congruent sides make congruent triangles, the proving of this by definition actually takes a bit of work. This exercise steps the class through this kind of proof by...

High School geometers verify through experimentation certain properties about dilations. This multi-step problem challenges them to construct examples of dilations to verify specific facts, the final step provides an opportunity to more...

Geometers explore symmetries of isosceles triangles by using rigid transformations of the plane. They complete four tasks, including congruence proofs, which illustrate the relationship between congruence and rigid transformations. The...

Learners see application of construction techniques in a short but sophisticated problem. Combining the properties of inscribed triangles with tangent lines and radii makes a nice bridge between units, a way of using...

Intricate details of a modern technology that many of us take for granted in our phones, computers (and some cars) are laid bare in a short but deeply investigative activity. The math behind a seemingly simple GPS device...

Triangle centers and the segments that create them easily become an exercise in memorization, without the help of engaging applications like this lesson. Here the class investigates the measure of center that is equidistant to the three...

This Oswego City School District Regents Exam Prep site shows you how to proof something by showing that it is false. This look at indirect proofs includes a practice and a teacher resource page, which features a warm-up activity.

Find out the general form for two column proofs, flow proofs, and paragraph proofs here. The site is very brief and discusses each type of proof using the same example.

This applet proves the Pythagorean Theorem "without words" using geometry.

Twenty-five problems cover the topic of logic and proof in different geometry settings. They are given with each step to the solution cleverly revealed one at a time. You can work each step of the problem then click the "View Solution"...

A geometry problem for students to use their mathematical reasoning skills to explain a right triangle property.

This site offers a brief description and an example of a paragraph proof. And remember, "there is never just one way of stating a proof," so others are mentioned as well.

This activity introduces students to the terms of hypothesis, conclusion, conditional, converse, inverse, contrapositive, and biconditional using popular advertising slogans. A learning check activity is used to check their understanding...

A geometry proof problem involving a right triangle and finding angles of equal measure.

This is a proof problem, considered a "three star" geometry problem requiring knowledge of proofs and properties of circles to solve this equal area of inscribed polygons problem.

This is a "three star" geometry problem where prior knowledge of problem solving and thinking through proofs is recommended to solve this trapezoid inscribed in a semicircle problem.

A geometry proof involving exterior angles of a triangle.