Question

geometry: concepts & connections unit 3 georgias k - 12 mathematics standards
image 3

1. what sequence of rigid motions maps △dgl to △cnb?
2. which parts of the triangles in image 3 must be congruent? write the congruent parts preimage and image.

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Explanation:

Step1: Analyze rigid - motion for question 8

Rigid motions include translations, rotations, and reflections. By observing the position of △DGL and △CNB, a reflection over the y - axis flips △DGL to the right - hand side of the y - axis, and then a translation of (x,y - 7) moves it down to match △CNB.

Step2: Recall congruence in rigid motions for question 9

Rigid motions preserve distance and angle measure. So, when one triangle is mapped to another by rigid motions, corresponding sides and angles are congruent. We identify corresponding parts based on the mapping of vertices (D to C, G to N, L to B).

Answer:

1. Reflection over the y - axis followed by a translation of (x,y - 7)
2. Since a rigid motion maps △DGL to △CNB, the corresponding sides and angles are congruent.

• Corresponding sides: $\overline{DG}\cong\overline{CN}$, $\overline{GL}\cong\overline{NB}$, $\overline{DL}\cong\overline{CB}$
• Corresponding angles: $\angle D\cong\angle C$, $\angle G\cong\angle N$, $\angle L\cong\angle B$