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. ( angle r ) corresponds to ( angle pqq ). ( angle pqr ) corresponds to ( angle qpq ). segment ( qq ) is parallel to segment ( pp ). side rq corresponds to side ( qq ). ( \triangle pqrcong\triangle pqq )

Explanation:

Step1: Analyze angle correspondence

• For similar triangles, corresponding angles are equal. In \(\triangle PQR\) and \(\triangle P'Q'Q\), \(\angle R\) and \(\angle P'QQ'\) are corresponding angles as the dilation preserves the shape and the relative position of angles.
• Also, side \(RQ\) in \(\triangle PQR\) and side \(QQ'\) in \(\triangle P'Q'Q\) are corresponding sides as per the dilation rule \(D_{O,2}(x,y)\to(2x,2y)\) which maps the pre - image to the image.

Step2: Check other options

• \(\angle PQR\) does not correspond to \(\angle QPQ'\) as their positions and relationships in the triangles are not in line with the dilation - induced similarity.
• Segment \(QQ'\) is not parallel to segment \(PP'\) as their slopes (if calculated from the grid) are different.
• \(\triangle PQR\) and \(\triangle P'Q'Q\) are similar (\(\triangle PQR\sim\triangle P'Q'Q\)) not congruent (\(\triangle PQR

ot\cong\triangle P'Q'Q\)) since dilation changes the size (by a scale factor of \(2\) here).

Answer:

\(\angle R\) corresponds to \(\angle P'QQ'\) and Side \(RQ\) corresponds to side \(QQ'\)