In the given figure, AB = AC and BD = EC then prove that ΔADE is an i

1.	In the given figure, AB = AC and BD = EC then prove that ΔADE is an isosceles triangle.
Answer» In ΔABD and ΔAEC AB = AC (given) …(i) ∠ABC = ∠ACB …(ii) (angle opposite to equal sides are equal) Also BD = EC (given) …(iii) From (i), (ii) and (iii), we have ΔABD = ΔAEC (by SAS congruency property) ⇒ AD = AE (by c.p.c.t) Hence, ΔADE is an isosceles triangle. Hence proved.

In the given figure, AB = AC and BD = EC then prove that ΔADE is an isosceles triangle.

Answer»

In ΔABD and ΔAEC

AB = AC (given) …(i)

∠ABC = ∠ACB …(ii) (angle opposite to equal sides are equal)

Also BD = EC (given) …(iii)

From (i), (ii) and (iii), we have

ΔABD = ΔAEC (by SAS congruency property)

⇒ AD = AE (by c.p.c.t)

Hence, ΔADE is an isosceles triangle.

Hence proved.