Question

In Fig., it is given that AB = BC and AD = EC. Prove that
(i) ​

Answer 1

Given:-

• AB = BC,
• AD = EC

TO Proof:-

• ∆ABE ≅ ∆CBD
• BD = BE

Proof:-

(i) In ∆ABC,

∵ AB = BC    | Given

∴ ∠BAC = ∠BCA  ____(1)

| Angles opposite to equal sides of a triangle are equal |

AD = EC    | Given

⇒ AD + DE = EC + DE

⇒ AE = CD  ___..(2)

Now, in ∆ABE and ∆CBD,

AE = CD    | From (2)

AB = CB    | Given

∠BAE = ∠BCD    | From (1)

∴ ∆ABE ≅ ∆CBD | SAS congruence rule.

(ii) BD = BE ( by CPCT)