In quadrilateral

MATHEMATICS · Multi-part · CBSE · Mathematics · Quadrilaterals · Quadrilaterals

Problem

In quadrilateral

ABCD

, the diagonal

AC

divides it into two congruent triangles, that is,

\triangle ABC \cong \triangle CDA

. (i) Prove that

AB = CD

. (ii) Prove that

AB \parallel CD

. (iii) Hence show that

ABCD

is a parallelogram. (iv) If

AB = 5\,\text{cm}

and

BC = 3\,\text{cm}

, find the perimeter of

ABCD