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 4 · 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.

$A coordinate grid showing triangle GHI pointing right and a congruent dashed triangle JKL pointing up, sharing the origin.$

Triangle $GHI$ has vertices $G(0, 0)$ , $H(3, 0)$ , $I(1, 2)$ . Triangle $JKL$ has vertices $J(0, 0)$ , $K(0, 3)$ , $L(-2, 1)$ . They share the vertex $G = J$ . Which single rigid motion maps $GHI$ onto $JKL$ ?

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

A translation $3$ units up.

A reflection across the x-axis.

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