Geometric Proof Teacher Resources

Looking to challenge your students that have mastered basic triangle congruence proofs? A collection of proofs employ previously learned definitions, theorems, and properties. Pupils draw on their past experiences with proofs to...

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...

Challenge the class to prove that the dilation properties always hold. The lesson develops an informal proof of the properties of dilations through a discussion. Two of the proofs are verified with each class member performing the...

Prove the Pythagorean Theorem using multiple informal proofs. Scholars first develop an understanding of the origins of the Pythagorean Theorem through proofs. They round out the lesson by using the theorem to find missing side lengths...

Why is it a two-column proof? A video introduces the class to the concept of a two-column proof and how to set one up. The segment of a playlist on basic geometry highlights the types of reasons that can be in a proof.

Connect algebra and geometry on the coordinate plane. The eighth unit in a nine-part integrated course has pupils develop the distance formula from the Pythagorean Theorem. Scholars prove geometric theorems using coordinates...

Your class knows the Pythagorean Theorem, but can they prove it? A series of three videos shows two proofs of the Pythagorean Theorem and use it to classify 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...

There is more than one way to prove the Pythagorean Theorem. Euclid and Einstein found the same way to prove the Pythagorean Theorem. The video introduces several other ways to prove the theorem along with the history of its use.

Can you prove it? Lead your class through the development of the Side Splitter Theorem through proofs. Individuals connect the ratio and parallel method of dilation through an exploration of two proofs. After completing the proofs,...

What does it take to show two triangles are similar? The 11th segment in a series of 16 introduces the AA Criterion for Similarity. A discussion provides an informal proof of the theorem. Exercises and problems require scholars to apply...

Discover a new application of the Pythagorean Theorem. Learners prove and apply the converse of the Pythagorean Theorem in the 17th lesson plan in a 25-part series. The examples ask learners to verify right triangles using the...

If angles intercept the same arc, the angles must be the same size. The quick video talks through the proof of showing the reason two inscribed angles that intersect the same arc have the same measurement. Pupils then create their own...

How do you know if a pair of triangles are congruent? Use the lesson to help class members become comfortable identifying the congruence criteria. They begin with an exploration of ASA and SSS criteria through transformations and...

Scholars observe a video explaining the alternate segment theorem proof. Then, they apply the theorem to additional practice problems from the text and complete a worksheet.

Prove the best way to keep up in Geometry. Scholars first review algebraic properties from Algebra. Learners then use the properties to create two-column proofs to solve linear equations before completing algebraic proofs by providing...

You've heard that it is true, but can you prove it? Scholars learn the Pythagorean Theorem through proof. After an overview of proofs of the theorem, learners apply it to prove triangles are right and to problem solve. This is the second...

Triangles bring sums to geometry. The lesson presents two theorems dealing with the angles of a triangle. Pupils learn about the Triangle Sum Theorem and the Exterior Angle Theorem, and then apply the theorems to create equations and...

Your class may believe that geometry is a trial, but they don't know how right they are. A thorough math lesson combines the laws of logic with the laws of geometry. As high schoolers review the work of historical mathematicians and...

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...

Triangles are all about threes, and practicing proving postulates is a great way to get started. The first page of the instructional activity provides a brief introduction of the different properties and postulates. The remaining...

Just what does it take to show two rhombuses are similar? The assessment task asks pupils to develop an argument to show that given quadrilaterals are rhombuses. Class members also use their knowledge of similar triangles to show two...

Show more than one way to prove similarity. Scholars learn three different methods to show two triangles are similar, Angle-Angle, Side-Side-Side, and Side-Angle-Side. Pupils practice applying these methods to determine whether two given...

Medians, midsegments, altitudes, oh my! Pupils study the properties of the median of a triangle, initially examining a proof utilizing midsegments to determine the length ratio of a median. They then use the information to find missing...