Is a parallelogram whose diagonals and intersect at .

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

Problem

ABCD

is a parallelogram whose diagonals

AC

and

BD

intersect at

O

. (i) Show that

\triangle AOB \cong \triangle COD

and name the congruence criterion used. (ii) Using the result of part (i), prove that

OA = OC

and

OB = OD

. (iii) What do you conclude about point

O

with respect to the diagonals

AC

and

BD

? Give a brief proof for your conclusion.