Question

In the figure, P, Q, R and S are respectively the mid-points of the sides of the quadrilateral ABCD. Prove that O is the mid-point of both PR and QS.​

Answer 1

Answer:

In the figure, P, Q, R and S are respectively the mid-points of the sides of the quadrilateral ABCD. Prove that O is the mid-point of both PR and QS.Answer:

ANSWER

P,Q,R and S are the mid-point of the sides AB,BC,CD and DA of a quadrilateral ABCD.

⇒ AC=BD

In △ABC,

P and Q are the mid-points of the sides AB and BC respectively.

∴ PQ∥AC ----- ( 1 )

And PQ=

2

1

×AC ------ ( 2 )

Similarly, SR∥AC and SR=

2

1

×AC ----- ( 3 )

From ( 1 ), ( 2 ) and ( 3 ) we get,

⇒ PQ∥SR and PQ=SR=

2

1

×AC ----- ( 4 )

Similarly we an show that,

⇒ SP∥RQ and SP=RQ=

2

1

×BD ----- ( 5 )

Since, AC=BD

∴ PQ=SR=SP=RQ [ From ( 4 ) and ( 5 ) ]

All sides of the quadrilateral are equal.

∴ PQRS is a rhombus.

solution

Answer 2

Answer:

okokok

Step-by-step explanation:

because if both are having four sides means P Q R and S then you can also imagine that these all are like something edge of the quadrilateral as ABCD so is the midpoint because it can be in the middle only so all thanks mark me as brainliest