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:

m∠p ≅ m∠l; this can be confirmed by translating point p to point l.

step-by-step explanation:

"aa similarity" means that when two angles are equal, the triangles are similar.

in δlmn ~ δpqr, we already know both m∠m = m∠q because m∠m (aka m∠lmn).

δpqr was dilated from δlmn from ∠m as the center of dilation, m∠m = m∠q.

pqr and lmn are written in the order of their equivalent angles.

p = l

q = m

r = n

if you translate point p to point l, the path stays on the side of the triangle, proving that the angle has not changed.

answer: it's d

step-by-step explanation: