Question

choose all of the equations that represent correct comparisons between triangle pqr and triangle pqr. a. (overline{pr}=overline{pr}) b. (overline{pr}=3\timesoverline{pr}) c. (mangle prq = mangle prq) d. (mangle prq=3\times mangle prq)

Explanation:

Step1: Recall dilation properties

When a triangle is dilated, corresponding angles are equal and corresponding side - lengths are in proportion. If the scale factor of dilation is \(k\), the length of a side of the dilated triangle is \(k\) times the length of the corresponding side of the original triangle. Here, the scale factor \(k = 3\).

Step2: Analyze side - length relationship

For side - lengths, if \(\triangle PQR\) is dilated to \(\triangle P'Q'R'\) with a scale factor of \(3\), then \(\overline{P'R'}=3\times\overline{PR}\), so option B is correct.

Step3: Analyze angle relationship

For angles, since dilation is a similarity transformation, corresponding angles are congruent. So \(m\angle P'R'Q'=m\angle PRQ\), and option C is incorrect. Also, \(m\angle P'R'Q'
eq3\times m\angle PRQ\), so option D is incorrect. And \(\overline{P'R'}
eq\overline{PR}\), so option A is incorrect.

Answer:

B. \(\overline{P'R'}=3\times\overline{PR}\)