Question

10.ABCD is a quadrilateral in which AB=AD and the angles B and D are both obtuse and equal to one another. Show that BC=CD .​

Answer 1

Answer:-

Construction: Let us join A with C. We can see two triangles formed - △ABC and △ADC.

In △ABC and △ADC,

1. AB = AD (Given)
2. ∠B = ∠D (Given)
3. AC = AC (Common side)

∴△ABC ≅ △ADC by SAS congruence criterion.

So,

BC = CD (by c.p.c.t.)

Hence, Proved.