EngageNY
Congruence, Proof, and Constructions
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 is broken...
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...
Shmoop
Coordinate Proofs
How do you know you know? Prove it! The guide goes through several examples and includes a link to a video to teach learners how to work through coordinate proofs. The goal is to prove that different shapes are indeed that shape.
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...
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...
EngageNY
Pythagorean Theorem, Revisited
Transform your pupils into mathematicians as they learn to prove the popular Pythagorean Theorem. The 16th instructional activity in the series of 25 continues by teaching learners how to develop a proof. It shows how to prove the...
Illustrative Mathematics
Equal Area Triangles on the Same Base II
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,...
EngageNY
Converse of the Pythagorean Theorem
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 of the...
Illustrative Mathematics
Joining Two Midpoints of Sides of a Triangle
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 lines cut...
EngageNY
Looking More Carefully at Parallel Lines
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...
EngageNY
Angle Sum of a Triangle
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...
Thomson Brooks-Core
Complex Numbers
A straightforward approach to teaching complex numbers, this lesson addresses the concepts of complex numbers, polar coordinates, Euler's formula, De moivres Theorem, and more. It includes a practice problems set with odd answers and a...
Illustrative Mathematics
Placing a Fire Hydrant
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...