Question

Can someone check my answers?

Answer 1

1. given
2. vertical angle congruence
3. AA similarity theorem

Explanation:

1. ∠C ≅ ∠E . . . . given

2. ∠ABC ≅ ∠DBE . . . . vertical angle congruence theorem

3. ΔABC ~ ΔDBE . . . . AA similarity theorem

_____

When showing similarity of triangles with no marked sides, theorems that involve sides (SSS, SAS, AAS) do not apply. The only theorem you can invoke is the AA similarity theorem.

A proof generally begins by restating those things that are "given," that form the basis for the rest of the proof. Here, the arcs on the diagram show that angles C and E are congruent. That is "given."