Question

consider figure abcd.
figure abcd is the image of figure abcd under a dilation with center a and scale factor 1/3.
which statements about figure abcd are true?
select three that apply.
a (overline{ab}) is parallel to (overline{dc})
b (overline{ad}) is parallel to (overline{bc})
c the measure of (angle a) is (33^{circ})
d the measure of (angle d) is (81^{circ})
f the length of (overline{ab}) equals the length of (overline{ab})

Explanation:

Step1: Properties of Dilation

Dilation preserves parallelism and angle measures.

Step2: Analyze Option A

Since \(AB\parallel DC\) in \(ABCD\), after dilation \(A'B'\parallel D'C'\) (dilation preserves parallelism).

Step3: Analyze Option B

In \(ABCD\), \(AD\) is not parallel to \(BC\). Dilation does not create new parallel relationships that did not exist in the original figure. So \(A'D'\) is not parallel to \(B'C'\).

Step4: Analyze Option C

Dilation preserves angle measures. \(\angle A = 99^{\circ}\), so \(\angle A'=99^{\circ}
eq33^{\circ}\)

Step5: Analyze Option D

Dilation preserves angle measures. \(\angle D = 81^{\circ}\), so \(\angle D'=81^{\circ}\)

Step6: Analyze Option E

Dilation with scale factor \(\frac{1}{3}\). If \(AB = x\), then \(A'B'=\frac{1}{3}x
eq x\)

Answer:

A. \(\overline{A'B'}\) is parallel to \(\overline{D'C'}\), D. The measure of \(\angle D'\) is \(81^{\circ}\)