Question

In Figure, it is given that AB=CE EF= BD and AFE= angle CBD . Prove that triangle AFE cong triangle CBD​

Answer 1

To prove that triangle AFE is congruent to triangle CBD, we can use the Side-Angle-Side (SAS) congruence criterion.

Here are the steps to prove the congruence:

1. Given: AB = CE, EF = BD, and ∠AFE = ∠CBD.

2. We need to show that triangle AFE is congruent to triangle CBD.

3. Start by identifying the shared side: EF.

4. Next, identify the corresponding angles: ∠AFE and ∠CBD.

5. Finally, identify the remaining side: AB = CE and BD.

6. Since we have the shared side EF, the congruent angles ∠AFE = ∠CBD, and the remaining sides AB = CE and EF = BD, we can apply the SAS congruence criterion.

7. By the SAS congruence criterion, triangle AFE is congruent to triangle CBD.

8. Therefore, triangle AFE ≅ triangle CBD.

By following the steps above and applying the SAS congruence criterion, we have proven that triangle AFE is congruent to triangle CBD.

Explanation: