Back to Understand that a two-dimensional figure is congruent to another if the second can be obtained from the first by a sequence of rotations, reflections, and translations — Problem 3 · Task Set 22

Exercises: Congruence Through Sequences of Rigid Motions

Work through each section in order. When you describe a sequence of rigid motions, name each transformation in order and give its parameters: direction and distance for a translation, the line of reflection for a reflection, and the center and angle (with direction) for a rotation. Two figures are congruent only when a sequence of rigid motions maps one exactly onto the other.

Grade 8·21 problems·~35 min·Common Core Math - Grade 8·container·8-g-a-2

Work through problems with immediate feedback

Recall / Warm-Up

These problems review skills you already know: performing single rigid motions and comparing measurements.

Two triangles have side lengths of $3$ , $4$ , $5$ and $3$ , $4$ , $5$ . A third triangle has side lengths $3$ , $4$ , $6$ . Rigid motions never change a length. Which pair of triangles could possibly be congruent?

The two triangles with sides $3$ , $4$ , $5$ , because all their corresponding lengths match.

The $3$ , $4$ , $5$ triangle and the $3$ , $4$ , $6$ triangle, because they share two side lengths.

No two of these triangles could ever be congruent.

Any two triangles are congruent as long as they are both triangles.