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 1 · Task Set 61

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.

$A coordinate grid with triangle ABC on the left and a congruent dashed triangle DEF the same shape farther right.$

Triangle $ABC$ has vertices $A(1, 1)$ , $B(4, 1)$ , $C(2, 3)$ . Triangle $DEF$ has vertices $D(7, 1)$ , $E(10, 1)$ , $F(8, 3)$ . Which single transformation maps $ABC$ onto $DEF$ ?

A translation 6 units to the right.

A reflection across the y-axis.

They look alike, so no transformation is needed to call them congruent.

A rotation of $90\degree$ about the origin.