Question

In completing the following proof, which of the following statements should be included?

Given: regular ΔDAF; midpoints B, C, E; ∠DBE ≅ ∠FCE
Prove: DB ≅ FC

Answer 1

Option (2) CPCTC

Explanation:

In the given regular triangle ADF, all sides and angles of the triangle will be equal

∠A = ∠D = ∠F = 60°

And DE = EF [Since E is the midpoint of side DF]

Statements Reasons

1). ∠D ≅ ∠F Given

2). ∠DBE ≅ ∠ECF Given

3). DE ≅ EF Given

4). ΔDBE ≅ ΔECF By AAS property

Therefore, DB ≅ FC

Option (2) Corresponding parts of the congruent triangles are congruent (CPCTC)