Question

ABCD is a quadrilateral in which P,Q,R and S are mid point of the sides AB,BC, and DA (see fig,29) AC is a diaogonal.show that

Answer 1

Heya....

1) In triangle ADC
S is the mid point of AD (given)
R is the mid point of DC (given)
By mid point theorem,
➡SR || AC and SR = 1/2 AC ..........(1)

2) In triangle ABC
P is the mid point of AB (given)
Q is the mid point of BC (given)
By mid point theorem,
PQ || AC and PQ = 1/2 AC ..........(2)
From (1) and (2)
➡ SR= PQ ......(3)
SR||PQ.....(4)

3)SR= PQ and SR||PQ (from (3) and (4))
➡ Thus PQRS is a parallelogram as one pair of opposite sides are equal and parallel.