Question

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solve it.....​

Answer 1

☆Given:-

ABCD is a quadrilateral in which P,Q,R,S are mid-points of the sides AB,BC,CD,DA. AC is a diagonal.

☆To prove:-

i.SR||AC and SR=1/2AC

ii.PQ=SR

iii.PQRS is a parallelogram.

☆Solution:-

In triangle ABC,the points P and Q are the midpoints of AB and BC respectively.

=>PQ||AC and PQ=1/2AC (by mid-point theorem)

Again in triangle DAC,the points S and R are the midpoints of AD and DC respectively.

=>SR||AC and SR=1/2AC (by mid-point theorem)

Now,PQ||AC and SR||AC

=>PQ||SR

=>PQ=SR (each equal to 1/2AC)

Thus,PQ||SR and PQ=SR

Hence,PQRS is a parallelogram.

Answer 2

Step-by-step explanation:

☆Given:-

• ABCD is a quadrilateral in which P,Q,R,S are mid-points of the sides AB,BC,CD,DA. AC is a diagonal.

☆To prove:-

i.SR||AC and SR=1/2AC

ii.PQ=SR

iii.PQRS is a parallelogram.

☆Solution:-

• In triangle ABC,the points P and Q are the midpoints of AB and BC respectively.

=>PQ||AC and PQ=1/2AC (by mid-point theorem)

• Again in triangle DAC,the points S and R are the midpoints of AD and DC respectively.

=>SR||AC and SR=1/2AC (by mid-point theorem)

Now,PQ||AC and SR||AC

=>PQ||SR

=>PQ=SR (each equal to 1/2AC)

Thus,PQ||SR and PQ=SR

Hence,PQRS is a parallelogram.

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