Question

ABCD is a quadrilateral in which P, Q, R, and S are the mid points of the side AB, BC, CD and DA. AC is a diagonal . show that
1)SR// and SR=1/2AC
2)PQ=SR
3)PQRS is a parallelogram

Answer 1

Answer:

PQ parallel to AC and PQ=1/2AC ( by mid point theorem)

again in DAC, the point SR are the midpoint of AD and DC respectively.

SR parallel AC and SR=1/2 AC ( by midpoint theorem).

now, PQ parallel AC and SR parallel AC = PQ parallel SR.

also, PQ= SR ( each equal to 1/2 AC).

PQ parallel SR and PQ= SR.

hence PQRS is a Parraleogram.

Explanation:

I hope it's help you lot ...

please mark me brainlist

please follow me........

Answer 2

Explanation:

The Midpoint Theorem states that the segment joining two sides of a triangle at the midpoints of those sides is parallel to the third side and is half the length of the third side.

(i) In △DAC , S is the mid point of DA and R is the mid point of DC. Therefore, SR∥AC and SR=

$\frac{1}{2}$AC.By mid-point theorem.

(ii) In △BAC , P is the mid point of AB and Q is the mid point of BC. Therefore, PQ∥AC and PQ=$\frac{2}{1}$

AC.By mid-point theorem. But from (i) SR=$\frac{1}{2}$AC therefore PQ=SR

(iii) PQ∥AC & SR∥AC therefore PQ∥SR and PQ=SR. Hence, a quadrilateral with opposite sides equal and paralle is a parallelogram. Therefore PQRS is a parallelogram.

xXitzSweetMelodyXx