Geometers prove that triangle PQR is congruent to triangle ABC by describing any combination of rotations, reflections, and translations that would prove it so. There is only this single task on the handout, but a detailed explanation of...

Two triangles are displayed on a coordinate plane. Youngsters apply a reflection and a translation to demonstrate their congruence. This exercise makes a terrific tool for teaching these concepts, or a way to assess learning.

The problem seems simple: find the area of the equilateral triangle whose sides are each length 1. In fact, this same problem is solved in 8th grade, addressing a different Common Core standard, using the formula for area of a triangle...

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...

Try five problems on triangles. Levels A and B focus on shapes that can be created from right triangles. Level C touches upon the relationship between the area of a six-pointed star and the area of each triangle of which it is composed....

A triangle rests in quadrant two, from which your class members must draw reflections, both over x=2 and x=-2. This focused exercise strengthens students' skills when it comes to reflection on the coordinate plane.

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...

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...

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...

One of the basic properties of inscribed angles gets a triangle proof treatment in a short but detailed exercise. Leading directions take the learner through identifying characteristics of a circle and how they relate to angles and...

Your learners will make good use of the Socratic method in a collaborative task that begins with an assumed solution and ends with deeper understanding of the idea of determining two triangles congruent.

The task at hand is to partition a hexagon into two, four, and eight congruent figures. Make sure to give your wizards a sheet of triangle grid paper on which to decompose the hexagons. Have them explain which rotations, reflections, or...

After learning that the sum of interior angles for triangles is 108 degrees, take it further to show that the sum of angles in any polygon is the same! Using hexagons, pupils practice finding the measure of the six congruent angles. Make...

This can be used as a critical thinking exercise in congruence or as a teaching tool when first introducing the concept. Four octagons are arranged in such a way that a square is formed in the middle. With this information, geometry...

Your learners collaboratively find the lines of symmetry in an equilateral triangle using rigid transformations and symmetry. Through congruence proofs they show that they understand congruence in terms of rigid motions as they...

This is an interesting geometry problem. Given the figure, find the area of a triangle that is created by the intersecting lines. The solution requires one to use what he/she knows about coordinate geometry, as well as triangle...

Young geometers become pool sharks in this analysis of the angles and lengths of a trick shot. By using angles of incidence and reflection to develop similar triangles, learners plan the exact placement of balls to make the shot....

Participants who use this resource will apply the Pythagorean Theorem to show whether or not the shaded triangle inscribed in a rectangle is a right triangle. Once all of the sides on the shaded triangle are found, it is important that...

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...

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...

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...

Your geometry learners are guided by questions that help them use the language of reflections to explain the Side-Angle-Side congruence between two triangles in this collaborative task. Given a sample solution, declaring the...

Inscribing a square in a circle brings up a number of interesting geometry topics including triangle congruence and how to prove a quadrilateral is a square. This activity is followed up by finding the area of the square and determining...

Your geometry learners explore Angle-Side-Angle congruence in this collaborative task. The sum of the interior angles of all triangles being one hundred eighty degrees, is the key learners will discover as they explain their reasoning...