Question

triangle pqr was dilated according to the rule $d_{o,2}(x,y) \to (2x,2y)$ to create similar triangle $pqq$. which statements are true? select two options. $\square$ $\angle r$ corresponds to $\angle pqq$. $\square$ $\angle pqr$ corresponds to $\angle qpq$. $\square$ segment $qq$ is parallel to segment $pp$. $\square$ side $rq$ corresponds to side $qq$. $\square$ $\triangle pqr \cong \triangle pqq$

Explanation:

1. Check angle correspondence: In a dilation from center \(O\), \(\angle R\) (vertex \(R\) of \(\triangle PQR\)) maps to \(\angle P'QQ'\) (vertex \(Q\) of \(\triangle P'Q'Q\)) as the dilated figure's corresponding angle.
2. Check parallel segments: Segments connecting pre-image points to their dilated image points (like \(QQ'\) and \(PP'\)) from the same center of dilation are parallel, since they lie along rays from the dilation center.
3. Eliminate false statements:

• \(\angle PQR\) does not correspond to \(\angle QPQ'\) (incorrect vertex mapping).
• Side \(RQ\) does not correspond to \(QQ'\) (incorrect side mapping).
• \(\triangle PQR \cong \triangle P'Q'Q\) is false because dilation creates similarity, not congruence (size changes).

Answer:

• ∠R corresponds to ∠P'QQ'.
• Segment QQ' is parallel to segment PP'.