Mathematics

Problem

In quadrilateral

LMNO

, it is given that

LM = NO = 9\,\text{cm}

and

LM \parallel NO

. The diagonals

LO

and

MN

intersect at

P

. a. (i) Prove that

LMNO

is a parallelogram. b. (ii) Show that

P

is the midpoint of both the diagonals. c. (iii) If

LP = 5\,\text{cm}

, find the lengths of

LO

and

PO