Question

In the given figure, equal sides and angles have been marked by the same signs. Prove that $∆ABC\cong ∆BAD$ and hence find the angles equal to $\angle ACB$ and $\angle CAB$.

Answer 1

STEP 1 : Proving that $∆ABC\cong ∆BAD$

In $∆ABC$ and $∆BAD$,

$AB=BA$ [ Common Side ]

$\angle ABC=\angle BAD$ [ Given ]

$BC=AD$ [Given ]

Therefore, by SAS congruence condition $∆ABC\cong ∆BAD$

STEP 2 : Finding the angles equal to $\angle ACB$ and $\angle CAB$

Since $∆ABC\cong ∆BAD$

We know that, corresponding parts of congruent triangles are equal.

Therefore,

$\angle ACB=\angle BDA$ [ By C.P.C.T. ]

$\angle CAB=\angle DBA$ [ By C.P.C.T. ]