Question

From the given figure prove that i) ΔABC and ΔDEF are congruent ii) A F = DC

Answer 1

9514 1404 393

Step-by-step explanation:

1. ∠ABC ≅ ∠DEF ≅ 90° . . . . given

2. BC ≅ FE, BC║FE . . . . given

3. ∠BCF ≅ ∠EFC . . . . alternate interior angles

4. ΔABC ≅ ΔDEF . . . . ASA

5. CA ≅ FD . . . . CPCTC

6. FC ≅ CF . . . . reflexive property of congruence

7. CA -CF ≅ FD -FC . . . . addition property of equality

8. FA ≅ CD . . . . segment sum theorem