Quadrilateral has its diagonals and intersecting at the point

MATHEMATICS · Subjective · CBSE · Mathematics · Triangles · Triangles

Problem

Quadrilateral

ABCD

has its diagonals

AC

and

BD

intersecting at the point

O

. It is given that

AO = CO

BO = DO

and

\angle AOB = \angle COD

. (a) Prove that

\triangle AOB \cong \triangle COD

. (b) Prove that

\triangle BOC \cong \triangle DOA

. (c) Using the results of parts (a) and (b), explain why

AB = CD

and

AD = BC

. Give clear reasons for every statement you make.