Question

Given: ABC and EDC, C is the midpoint of BD and AE
Prove: AB II DE

Answer 1

Explanation:

1. ΔABC=ΔCDE: a) according to the condition BC=CD and AC=CE; b) m∠(BCA)=m∠(DCE).

2. if ΔABC=ΔCDE, then m∠(BAC)=m∠(DEC) and m∠(ABC)=m∠(CDE).

3. if m∠(BAC)=m∠(DEC), then AB || DE (or if m∠(ABC)=m∠(CDE), then AB || DE).