Question

In quadrilateral ABCD , AB = BC , BD = CA . Prove that angle ADB = angle BCA and angle DAB = angle CBA

Answer 1

AB = BC
BD = AC
AB || CD
BC || AD
So it proves AB = CD and BC = AD
Angle BCA = Angle ADB
Since AC = BD, AD = BC and AB is common.
So it is a congruent triangles on basis of SSS theorem.
So, angle BCA is equal to angle ADB

Angle DAB = Angle CBA
Since AD = BC, AC = BD and AB is common.
So it is congruent triangle on basis of SSS theorem.
So, Angle DAB = Angle CBA

Answer 2

Here is the ans
Hope it helps you