Question

Shaun drew Î"LMN, in which m∠LMN = 90°. He then drew Î"PQR, which was a dilation of Î"LMN by a scale factor of 3 from the center of dilation at point M. Which of these can be used to prove Î"LMN ~ Î"PQR by the AA similarity postulate?

a.Segment LM = 3 times segment PQ; this can be confirmed by translating point P to point L.
b.Se(gment MN = 3 times segment QR; this can be confirmed by translating point R to point N.
c.m∠P ≅ m∠N; this can be confirmed by translating point P to point N.
d.m∠R ≅ m∠N; this can be confirmed by translating point R to point N.

Answer 1

To prove ΔLMN ~ ΔPQR by the AA similarity postulate, we need to show that the angles in the two triangles are congruent and the corresponding sides are proportional. Option c, m∠P ≅ m∠N, can be used to prove the triangles similar.

Step-by-step explanation:

To prove that ΔLMN ~ ΔPQR by the AA similarity postulate, we need to show that the angles in the two triangles are congruent and the corresponding sides are proportional.

Option c, m∠P ≅ m∠N, can be used to prove the triangles similar. If we translate point P to point N, we can see that the angle at N in ΔPQR is congruent to the angle at N in ΔLMN.

Therefore, option c can be used to prove ΔLMN ~ ΔPQR.