Quadrilateral has diagonals and intersecting at point such that and .

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

Problem

Quadrilateral

ABCD

has diagonals

AC

and

BD

intersecting at point

O

such that

AO = OC

and

BO = OD

. (i) Prove that

\triangle AOB \cong \triangle COD

. (ii) Using the result of part (i), show that

AB \parallel CD

and

AD \parallel BC

. (iii) Hence, identify the special name of quadrilateral

ABCD

and give a complete justification for your answer.