Question

36. Abcd is a quadrilateral in which p,q,r,s are the mid point of side ab, bc, cd and da. Ac is a diagonal. Prove that: i. Sr || ac and sr = ac ii. Pq = sr iii. Pqrs is a parallelogram.

Answer 1

Answer:

Step-by-step explanation: Given:In quadrilateral ABCD

P,Q,R,S are mid point of sides AB,BC,CD and DA respectively

T.P: 1 2 3

In triangle ADC,

SR is a line segment joining the mid point of DA and DC respectively

:. SR||AC ( mid point therom)

In triangle BAC

PQ is a line segment joining the mid point of BA and BC respectively.

PQ||AC (mid point therom)

pQ = half of AC

From 1 &2

SR=PQ

SR ||PQ

:. PQRS is a ||gram