In quadrilateral the diagonals and meet at such that and

MATHEMATICS · Subjective · CBSE · Mathematics · Triangles · Triangles

Problem

In quadrilateral

ABCD

the diagonals

AC

and

BD

meet at

O

such that

AO = CO

and

BO = DO

. The lengths of two sides are

AB = 6.5\,\text{cm}

and

BC = 4.8\,\text{cm}

. (a) Prove that

\triangle AOB \cong \triangle COD

. (b) Prove that

\triangle BOC \cong \triangle DOA

. (c) Using the conclusions of (a) and (b), determine the lengths of

CD

and

AD

. Show all steps clearly.