Answer:
- given
- vertical angle congruence
- AA similarity theorem
Step-by-step explanation:
1. ∠C ≅ ∠E . . . . given
2. ∠ABC ≅ ∠DBE . . . . vertical angle congruence theorem
3. ΔABC ~ ΔDBE . . . . AA similarity theorem
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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."
