Question

20. In the given figure, AB=BE and BC=BD. Prove that ∆ABC is congruent to ​∆EBD
With Explanation
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Answer 1

$\rightarrow$ AB = BE (Given)

$\rightarrow$ Angle CBA = Angle CBD

$\rightarrow$ BC = BD

$\fbox \orange{Hence, ∆ABC is congruent to ∆EBD}$

By SAS Congruence criteria.

Answer 2

Given: AB=BE, BC=BD and ∠B = 90°

To Prove: ΔABC ≅ ΔEBD

Proof:  In Δ ABC and ΔEBD-

                  AB=BE (given)

            ∠CBA=∠EBD (each 90)

                  BC = BD (given)

   ∴ΔABC ≅ ΔEBD (by SAS)

           Hence, proved.