Question

Please help me
Which two states would be needed to probe that Triangle ABC is similar to triangle AEF

Answer 1

The triangles ABC and AEF in the figure are similar (not congruent)

The two statements to prove the similarities of the triangles are (a) $\angle AEF \cong \angle ABC$ and (c) $\angle A \cong \angle A$

For two triangles to be similar, then the corresponding angles of the triangles must be congruent.

The above statement means that, the following congruence statements from the options are true:

$\angle AEF \cong \angle ABC$ and $\angle A \cong \angle A$

This is so, because both angles are corresponding angles of the triangles.

Hence, the two statements to prove the similarities of the triangles are (a) $\angle AEF \cong \angle ABC$ and (c) $\angle A \cong \angle A$

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