Question

these quadrilaterals are similar. what else do you know about the quadrilaterals? select an answer a ∠d = ∠p b their areas are equal. c their perimeters are the same. d overline{cb}=overline{on}

Explanation:

Step1: Recall properties of similar figures

Similar figures have equal corresponding angles and proportional corresponding sides. Their perimeters are proportional (not equal) and areas are proportional (not equal).

Step2: Analyze each option

• Option A: Since the quadrilaterals are similar, corresponding angles are equal. If \( \angle D\) and \( \angle P\) are corresponding angles (by order of similarity), \( \angle D=\angle P\).
• Option B: For similar figures, if the scale factor \(k

eq1\), area ratio \(=k^{2}
eq1\). So areas are not equal.

• Option C: Perimeter ratio \( = k

eq1\) (if \(k\) is the scale factor). So perimeters are not equal.

• Option D: \(CB = 3\) and \(ON=2\), so \(CB

eq ON\)

Answer:

A. \( \angle D=\angle P\)