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...

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.

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...

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,...

So many times the characteristics of triangles are presented as a vocabulary-type of lesson, but in this activity they are key to unraveling a proof. A unique attack on proving that an inscribed angle that subtends a diameter must be a...

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...

This task asks learners to prove that the segment joining the midpoints of two sides of a parallelogram is both congruent and parallel to an adjacent side of the parallelogram. The activity would be good to use in a discussion about how...

If both pairs of opposite sides of a quadrilateral are congruent, is the quadrilateral a parallelogram? This task asks learners to determine the answer and to support their answer with a proof. The resource includes a commentary for...

This investigation uses Cabri Jr. and a cleaver rotation of a triangle to "prove" that the angles in a triangle add up to 180. This could be used to reinforce triangles and paralled lines as well as introduce the concept of rotating an...