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 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

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Fluency Practice

For each pair of congruent figures, describe a sequence of rigid motions that maps the first onto the second. Name each transformation in order, with its parameters.

$A coordinate grid showing triangle ABC near the bottom and a congruent dashed triangle DEF directly above it.$

Triangle $ABC$ has vertices $A(1, 1)$ , $B(4, 1)$ , $C(2, 3)$ . Triangle $DEF$ has vertices $D(1, 6)$ , $E(4, 6)$ , $F(2, 8)$ . Describe a single rigid motion that maps $ABC$ onto $DEF$ , and explain why this proves $ABC \cong DEF$ .