Question

In the figure AC = BC, angle DCA =angle ECB and angle DBC= angle EAC. Prove that DC = EC.

Answer 1

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.

Answer 2

Hi dear friend..
See the attached file..


I hope it will help
✌️☺️