Question

Can any good guy can solve this for me please...

In figure, AC=BC, <DCA=<ECB and <DBC = <EAC.
Prove that BD = AE...

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Answer 1

B⚪NJ⚪UR ⓂATE...❗❗❗

Solution:-

Given : AC = BC, angle DCA = angle ECB and angle DBC = angle EAC

∠ DCA = ∠ ECB (Given)

Adding ∠ ECD to both sides, we get

∠ DCA + ∠ ECD = ∠ ECB + ∠ ECD

Addition property

∠ ECA = ∠ DCB.

AC = BC (Given)

∠ DBC = ∠ EAC (Given)

⇒ Δ DBC ≡ Δ EAC (By ASA postulate)

So, DC = EC (By CPCT)

Hence proved.