Question

in the adjoining figure,ABCD is a quadrilateral in which P, Q,R and S are mid points of AB,BC,CD and DA respectively. AC is its diagonal. Show that 1. SR||AC and SR=1/2 AC 2. PQ=SR 3. PQRS is a parallelogram.

Answer 1

hey mate
here's the solution

Answer 2

To Prove : 

(i) SR || AC and SR = 1 2 AC 

(ii) PQ = SR 

(iii) PQRS is a parallelogram 

Proof : 

(i) In ∆ABC, P is the mid-point of AB and Q is the mid-point of BC.

∴ PQ || AC and PQ = 1/ 2 AC …(1) [Mid-point theorem] 

In ∆ADC, R is the mid-point of CD and S is the mid-point of AD 

∴ SR || AC and SR = 1 2 AC …(2) [Mid-point theorem] 

(ii) From (1) and (2), we get PQ || SR and PQ = SR 

(iii) Now in quadrilateral PQRS, its one pair of opposite sides PQ and SR is equal and parallel. 

∴ PQRS is a parallelogram. Proved.

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