Question

1. in the picture, quadrilateral qrst is an image of quadrilateral qrst after a rotation. the center of rotation is s. (from unit 1, lesson 7)

a. what is the length of side st? explain how you know.
b. what is the measure of angle r? explain how you know.

Explanation:

a. Step1: Recall Rotation Property

Rotations preserve segment lengths (congruence). So \( ST = S T' \).

a. Step2: Analyze Given Length

Given \( S T' = 14 \), so \( ST = 14 \) (by rotation's congruence preservation).

b. Step1: Recall Rotation Angle Property

Rotations preserve angle measures (congruence). So \( \angle R=\angle R' \).

b. Step2: Identify Given Angle

Given \( \angle R = 68^\circ \), so \( \angle R' = 68^\circ \) (by rotation's angle preservation).

Answer:

a. The length of \( ST \) is \( 14 \) (because rotation preserves segment lengths, so \( ST = S T' = 14 \)).
b. The measure of \( \angle R' \) is \( 68^\circ \) (because rotation preserves angle measures, so \( \angle R'=\angle R = 68^\circ \)).