Question

1.
17. ABCD is a quadrilateral in which AD BC If P, Q, R, S be the mid-points of AB, C and
respectively, then show that PORS is a rhombus.
18. In an isosceles AABC, the base AB is produced both the ways to P and O such that AP,
that AAPC - ABCO .
BQ-AC
12​

Answer 1

Answer:

In △BAD, P and S are mid-points of AB and BD

⇒ PS∥AD and PS=

2

1

AD --- ( 1 ) [ By BPT ]

Similarly in △CAD,

⇒ OR∥AD and QR=

2

1

AD --- ( 2 )

From ( 1 ) and ( 2 ), we get

⇒ PS∥QR and PS=QR=

2

1

AD ------ ( 3 )

In △BDC, we get

⇒ SR∥BC and SR=

2

1

BC ----- ( 4)

And in △ABC

PQ∥BC and PQ=

2

1

BC ------ ( 5 )

⇒ PQ∥SR, PQ=SR=

2

1

BC ---- ( 6 ) [ From ( 4 ) and ( 5 ) ]

∴ □PQRS is a parallelogram.

Now, AD=BC

∴

2

1

AD=

2

1

BC

∴ PS=QR=PQ=SR [ From ( 3 ) and ( 6 ) ]

∴ □PQRS is a rhombus.

Answer 2

Step-by-step explanation:

dear buddy the answer is correctly given by pravalka deedi.