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...

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...

Challenge the class with inscribed circles in triangles. The assessment task requests class members use their knowledge of circles and right triangles to prove two triangles are congruent. They go on to utilize their knowledge of...

Prove the Law of Sines two ways. The ninth segment in a series of 16 introduces the Law of Sines to help the class find lengths of sides in oblique triangles. Pupils develop a proof of the Law of Sines by drawing an altitude and a second...

Young geometers apply their deductive reasoning skills and knowledge of proving triangles congruent in a task that asks them to prove if a point lies on the perpendicular bisector of a segment, then it is equidistant from the endpoints...

The task, should your class decide to take it, is to list a series of reflections that transfer a line segment from one position to another. 

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...

A congruent triangles quiz challenges teenage mathematicians to complete a pair of geometric proofs. Each problem includes a picture of the triangles in question, a given set of information, and the five steps needed to finish the proof....

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...

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...

Can your classes apply the knowledge they have learned? Use this performance task to find out! Individuals use transformations to explain congruence and angle relationships within parallel lines to find missing values. They show what...

The Hopewell people of the central Ohio Valley used right triangles in the construction of earthworks. Pupils use the Pythagorean Theorem to determine missing dimensions of right triangles used by the Hopewell people. The assessment task...

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...

Does the symmetry and transitive property apply to similarity? The 10th segment in a series of 16 presents the class with a group of explorations. The explorations have pairs show that similarity is both symmetrical and transitive....

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...

Are pyramids and cones similar in definition to prisms and cylinders? By examining the definitions, pupils determine that pyramids and cones are subsets of general cones. Working in groups, they continue to investigate the relationships...

Explore different ways of proving some theorems about lines and angles. Some transformations are used.