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 instructional activity by using the theorem to find...

This amazingly extensive unit covers a wealth of geometric ground, ranging from constructions to angle properties, triangle theorems, rigid transformations, and fundamentals of formal proofs.  Each of the almost-forty lessons...

Provide your emerging mathematicians with the tools to learn as they incorporate auxiliary lines to solve unknown angle proofs in this continuing segment. They decipher information from a diagram to uncover the missing pieces and...

Lead the class in a Greek history lesson with a geometric twist. Pupils relate a short video about geometric properties to modern-day methods of solving for unknown angles. They discuss parallel line theorems and complete...

Circles are the foundation of many geometric concepts and extensions - a point that is thoroughly driven home in this extensive unit. Fundamental properties of circles are investigated (including sector area, angle measure, and...

Looking at numerous examples of triangles, each with different properties, geometers develop their understanding of congruency. They use the notation of a counter-example to disprove certain conjectures and prove geometric theorems and...

High schoolers explore trigonometric identities.   In this Algebra II instructional activity, students use graphing to verify the reciprocal identities.  Using Cabri Jr, high schoolers investigate the Pythagorean...

Transform your pupils into mathematicians as they learn to prove the popular Pythagorean Theorem. The 16th lesson in the series of 25 continues by teaching learners how to develop a proof. It shows how to prove the Pythagorean Theorem...

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...

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...

Lead by example. Pupils use software to investigate given measures of sides and angles to determine whether they create congruent triangles. Using the discovered triangle congruences, learners put together proofs.

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.

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

Assist your class with each angle of geometry as they use exterior angles to form linear pairs with adjacent interior angles. They cover multiple vocabulary terms and work practice problems, complete with justifications, before...

Your algebra learners interpret algebraic expressions, in order to compare their structures, using a geometric context. They also discern how the two expressions are equivalent and represent a pattern geometrically and algebraically.

Prove the Angle Sum Theorem of a triangle using parallel line and transversal angle relationships. Pupils create a triangle from parallel lines and transversals. They find angle measures to show that the angles of a triangle must total...

Students define inductive and deductive reasoning and write two column proofs. In this geometry lesson, students analyze arguments and draw conclusion. They define steps necessary to arrive at the correct answer when completing proofs.

Everyone's heard of Pythagoras, but who's Ptolemy? Learners test Ptolemy's Theorem using a specific cyclic quadrilateral and a ruler in the 22nd installment of a 23-part module. They then work through a proof of the theorem.

Use the parallel lines to find your way. After first reviewing geometric constructions and the relationships between angles formed by parallel lines and a transversal, young mathematicians write proofs for theorems relating to parallel...

Students investigate proofs used to solve geometric problems. For this geometry lesson, students read about the history behind early geometry and learn how to write proofs correctly using two columns. The define terminology valuable to...

What do Sherlock Holmes and geometry have in common? Why, it is a matter of deductive reasoning as the class learns how to justify each step of a problem. Pupils then present a known fact to ensure that their decision is correct.

Can you prove it? Making assumptions in geometry is commonplace. This resource requires mathematicians to prove the parallel line postulate through constructions. Learners construct parallel lines with a 180-degree rotation and then...

Young scholars 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.

Students identify various geometric shapes. Apply the given formulas to determine the volume of these shapes. Design their own container to conform to specifications provided. Use their knowledge of volume formulas and shapes to compute...