Question

lesson practice choose the correct answer. use the transformation below for questions 1 and 2. triangle abc is rotated 90° clockwise to create triangle edc. image of triangle abc and edc 1. which angle is congruent to ∠b? a. ∠bce b. ∠ecd c. ∠e d. ∠d 2. which side is congruent to \\(\overline{ac}\\)? a. \\(\overline{bc}\\) b. \\(\overline{ec}\\) c. \\(\overline{ed}\\) d. \\(\overline{dc}\\) use the coordinate plane below for questions 3–5. parallelogram qrst is reflected over the y-axis to create parallelogram qrst. image of coordinate plane with parallelogram 3. which angle is congruent to ∠s? a. ∠q b. ∠r c. ∠s d. ∠t 4. which side is congruent to \\(\overline{qt}\\)? a. \\(\overline{qt}\\) b. \\(\overline{st}\\) c. \\(\overline{qr}\\) d. \\(\overline{qr}\\) 5. \\(\overline{qr}\\) is parallel to \\(\overline{ts}\\). which side is parallel to \\(\overline{qr}\\)? a. \\(\overline{sr}\\) b. \\(\overline{st}\\) c. \\(\overline{qt}\\) d. \\(\overline{rs}\\)

Explanation:

Question 1

When a figure is rotated, corresponding angles are congruent. Triangle \(ABC\) is rotated \(90^\circ\) clockwise to form Triangle \(EDC\), so \(\angle B\) corresponds to \(\angle E\).

Rotation preserves side lengths, so corresponding sides are congruent. \(\overline{AC}\) in \(\triangle ABC\) corresponds to \(\overline{EC}\) in \(\triangle EDC\) after a \(90^\circ\) clockwise rotation.

A reflection over the \(y\)-axis preserves angle measures, so corresponding angles are congruent. \(\angle S\) in parallelogram \(QRST\) corresponds to \(\angle S'\) in \(Q'R'S'T'\).

Answer:

C. \(\angle E\)

Question 2