Question

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

segment LM = 3segment PQ; this can be confirmed translating point P to point L.
segment MN = 3segment QR; this can be confirmed translating point R to point N.
m∠P ≅ m∠N; this can be confirmed by translating point P to point N.
m∠R ≅ m∠N; this can be confirmed by translating point R to point N.

Answer 1

m∠R ≅ m∠N; this can be confirmed by translating point R to point N.

Answer 2

The correct option is:

m∠R ≅ m∠N; this can be confirmed by translating point R to point N.

Explanation:

ΔPQR, is a dilation of ΔLMN by a scale factor of 3 from the center of dilation at point M.

Which mean that the point M overlap the point Q, the point L translated to the point P and the point N to the the point R

So, ∠M=∠Q , ∠L=∠P , ∠N=∠R

And we should know that the dilation of triangles makes it similar.

And AA similarity postulate mean : the triangle will be similar when two pairs of corresponding angles are equal.

So, the correct answer will be the fourth option

m∠R ≅ m∠N; this can be confirmed by translating point R to point N.