Question

in the given figure if ac=ae AB=AD ANGLE BAD = ANGLE EAC THEN prove that angle ADE = ANGLE ABD

Answer 1

Given: In figure, AC = AE, AB = AD and ∠BAD = ∠EAC.

To Prove: BC = DE.

Proof: In ∆ABC and ∆ADE,

AB = AD | Given

AC = AE | Given

∠BAD = ∠EAC | Given

⇒ ∠BAD + ∠DAC = ∠DAC + ∠EAC

| Adding ∠DAC to both sides

⇒ ∠BAC = ∠DAE

∴ ∆ABC ≅ ∆ADE | SAS Rule

∴ BC = DE. | C.P.C.T.