Mathematics

Problem

In parallelogram

ABCD

, points

P, Q, R

and

S

are the midpoints of sides

AB, BC, CD

and

DA

respectively. a. (i) Prove that

PQ \parallel SR

and

PS \parallel QR

. b. (ii) Hence, show that quadrilateral

PQRS

is a parallelogram. c. (iii) Show that the area of

PQRS

is exactly half the area of

ABCD