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 is similar to Δpqr by the AA similarity postulate?

1) The corresponding angles of Δlmn and Δpqr are congruent.
2) The corresponding sides of Δlmn and Δpqr are proportional.
3) The corresponding angles of Δlmn and Δpqr are proportional.
4) The corresponding sides of Δlmn and Δpqr are congruent.

Answer 1

Option 1, stating that the corresponding angles of Δlmn and Δpqr are congruent, can be used to prove that the triangles are similar by the AA similarity postulate.

Step-by-step explanation:

To prove that Δlmn is similar to Δpqr by the AA similarity postulate, we need to show that two corresponding angles of the triangles are congruent. The AA similarity postulate states that two triangles are similar if two pairs of corresponding angles are equal, which provides enough information to conclude similarity, as corresponding sides will be proportional as a result. Since Δpqr is a dilation of Δlmn with a scale factor of one-half from the center at point m, the angles have remained unchanged, and we already have that m∠lmn=90° which would mean m∠pqr=90° as well.

Thus, option 1) The corresponding angles of Δlmn and Δpqr are congruent can be used to prove that Δlmn is similar to Δpqr by the AA similarity postulate. This makes option 2) and option 4) unnecessary for proving similarity by AA, and option 3) is incorrect since angles are congruent, not proportional.