Question

Given: BD ≅ DE, CD ≅ DF
Prove: BC ≅ EF

Answer 1

statements

1. BD ≅ DE

2. CD ≅ DF

3. ∠BDC ≅ ∠EDF

4. ▲BDC = ▲EDF

5. BC ≅ EF

reasons

1. given

2. given

3. definition of vertical angles

4. SAS

5. CPCTC

Explanation:

• vertical angles are equal
• SAS means side-angle-side — two triangles are congruent when they meet the "requirements" for SAS
• CPCTC means corresponding parts of congruent triangles are congruent — when two triangles are congruent, their corresponding parts are also congruent