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

Answer 1

Answer: A) m∠P ≅ m∠L; this can be confirmed by translating point P to point L.

Answer 2

Answer:

m∠P ≅ m∠L; this can be confirmed by translating point P to point L.

Step-by-step explanation:

Angle angle (AA) similarity postulate state that two triangles are similar if two of their corresponding angle is similar. The corresponding angle for each point of the triangles will be:

∠L=∠P

∠Q=∠M

∠N=∠R

Since the 2nd triangle made from dilation, it should maintain its orientation.

Option 1 is true, ∠P corresponds to ∠L. If you move/translate point P to point L, you can confirm it because their orientation is the same.

Option 2 is false, the triangle will be similar if ∠P=∠N but you can't confirm it with translation alone.

Option 3 and 4 definitely wrong because it speaking about length, not the angle.