Question

2
if polygon abcd rotates 70° counterclockwise about the origin to give polygon abcd, which relationship must be true?
a. ( mangle abc < mangle abc )

b. ( bb = dd )

c. ( mangle abc > mangle abc )

d. ( ad = ad )

Explanation:

Step1: Recall Rotation Properties

A rotation is a rigid transformation, meaning it preserves side lengths and angle measures of the polygon. So, corresponding sides and angles of the original and rotated polygon are equal.

Step2: Analyze Each Option

• Option A: Angles are preserved in rotation, so \( m\angle ABC = m\angle A'B'C' \), not less. Eliminate A.
• Option B: \( BB' \) and \( DD' \) are lengths of rotation segments, but there's no guarantee they are equal. Rotation preserves side lengths of the polygon, not these segments. Eliminate B.
• Option C: Angles are preserved, so \( m\angle ABC = m\angle A'B'C' \), not greater. Eliminate C.
• Option D: Since rotation preserves side lengths, \( A'D' \) (corresponding to \( AD \)) must equal \( AD \). This is true.

Answer:

D. \( A'D' = AD \)