Question

Ellie drew ΔLMN, in which m∠LMN = 90°. She then drew ΔPQR, which was a dilation of ΔLMN by a scale factor of one half from the center of dilation at point M. Which of these can be used to prove ΔLMN ~ ΔPQR by the AA similarity postulate?

Answer 1

To prove the similarity of ΔLMN and ΔPQR using AA similarity postulate, we need to show the congruence of corresponding angles and proportionality of corresponding sides. ΔLMN is a right triangle with m∠LMN = 90°. The dilation of ΔLMN by a scale factor of one half from point M implies the similarity of ΔLMN and ΔPQR.

Step-by-step explanation:

To prove that ΔLMN is similar to ΔPQR using the AA similarity postulate, we need to show that the corresponding angles of the triangles are congruent and the corresponding sides are in proportion.

1. Since m∠LMN = 90°, we know that it is a right triangle.

2. The dilation of ΔLMN by a scale factor of one half from the center of dilation at point M means that the corresponding angles of ΔPQR are congruent to the angles of ΔLMN, and the corresponding sides are in proportion.

Therefore, we can conclude that ΔLMN is similar to ΔPQR by the AA similarity postulate.