Question

recognizing necessary information for similarity
what additional information could be used to prove that △abc ~ △nml? check all that apply.
□ ∠b ≅ ∠m
□ △abc is a right triangle.
□ △abc was rotated and dilated by a scale factor between 0 and 1.
□ △abc was translated right and down.
□ ∠c ≅ ∠l

Explanation:

Step1: Analyze given triangles

△ABC and △NML are both right triangles (∠A=∠N=90°). For similarity, AA (two angles congruent) is needed.

Step2: Check ∠B≅∠M

If ∠B≅∠M, then with right angles, AA similarity holds. Valid.

Step3: Check △ABC is right triangle

△ABC is already shown as right (∠A=90°). No new info. Invalid.

Step4: Check rotation + dilation (0<scale<1)

Rotation (rigid) + dilation (non-rigid) preserve shape → similarity. Valid.

Step5: Check translation right/down

Translation is rigid (no dilation) → congruent, not similar (unless scale=1, but not stated). Invalid.

Step6: Check ∠C≅∠L

If ∠C≅∠L, then with right angles, AA similarity holds. Valid.

Answer:

∠B ≅ ∠M, △ABC was rotated and dilated by a scale factor between 0 and 1, ∠C ≅ ∠L