Question

Rowena is proving that AD ≅ EB. Which statement does the ♣ represent in her proof?

ΔACD ≅ ΔECB
ΔACD ≅ ΔEFD
ΔAFB ≅ ΔEFD
ΔAFB ≅ ΔECB

Answer 1

It is the first answer.

Answer 2

Explanation:

From the figure, it is given that AB≅ED, BC≅CD and ∠CAD≅∠CEB.

Now, from ΔACD and ΔECB, we have

Statements Reason

1. AB≅ED, BC≅CD Given

2. ∠CAD≅∠CEB. Given

3. AB=ED, BC=DC Definition of congruent segments

4. AB+BC=AC and Segment addition postulate

ED+DC=CE

5. ED+DC=AC and Substitution property

ED+DC=CE

6. AC=CE Substitution property

7. AC≅CE Definition of congruent segments

8. ∠C≅∠C Reflexive property

9. ΔACD≅ΔECB ASA rule of congruency

Hence proved.

Hence, option A is correct.