QIn the adjoining figure, P Q R and S are the mid-points ofAB, BC, CD

1.	QIn the adjoining figure, P Q R and S are the mid-points ofAB, BC, CD and AD respectively. Prove that PQRS is aparallelogram.
Answer» Step-by-step explanation: 8th Maths Mensuration Area of Trapezium P,Q,R,R, and S are respecti... MATHS avatar Asked on January 17, 2020 by Dipankar Manivannan P,Q,R,R, and S are respectively the mid-points of sides AB, BC, CD, And DA of a quadrilateral ABCD in which AC =BD, then PQRS is a RHOMBUS. EASY Share Study later 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.

QIn the adjoining figure, P Q R and S are the mid-points ofAB, BC, CD and AD respectively. Prove that PQRS is aparallelogram.

Answer»

Step-by-step explanation:

8th

Maths

Mensuration

Area of Trapezium

P,Q,R,R, and S are respecti...

MATHS

avatar

Asked on January 17, 2020 by

Dipankar Manivannan

P,Q,R,R, and S are respectively the mid-points of sides AB, BC, CD, And DA of a quadrilateral ABCD in which AC =BD, then PQRS is a RHOMBUS.

EASY

Study later

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=

×AC ------ ( 2 )

Similarly, SR∥AC and SR=

×AC ----- ( 3 )

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

⇒ PQ∥SR and PQ=SR=

×AC ----- ( 4 )

Similarly we an show that,

⇒ SP∥RQ and SP=RQ=

×BD ----- ( 5 )

Since, AC=BD

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

All sides of the quadrilateral are equal.

∴ PQRS is a rhombus.