Question

Q.5.) ABCD is a parallelograms, E&F are the mid point of
AB and CD respectively. GH is any line intersecting AD, EF, and BC at G, P and H
respectively. Prove that GP=PH..
Q. 6). The diagonal of a quadrilateral ABCD are perpendicular. Show that the quadrilateral, formed by joining the mid point of it's sides, is a rectangle.

Answer 1

Step-by-step explanation:

Since E and F are mid-points AB and CD respectively.

∴AE=BE=

2

1

AB and CF=DF=

2

1

CD

But, AB=CD

∴

2

1

AB=

2

1

CD⇒BE=CF

Also, BE∥CF [∵AB∥CD]

∴ BEFC is a parallelogram.

⇒BC∥EF and BE=PH ...(i)

Now, BC∥EF

⇒AD∥EF [∵BC∥AD as ABCD is a ∥

gm

]

⇒AEFD is a parallelogram

⇒AE=GP ...(ii)

But, E is the mid-point of AB.

∴AE=BE

⇒GP=PH [Using (i) and (ii)]

solution

Answered By

toppr

2133 Views

How satisfied are you with the answer?

This will help us to improve better

answr

Get Instant Solutions, 24x7

No Signup required

girl

More Questions by difficulty

EASY

MEDIUM

HARD

Practice important Questions

R.D. Sharma Solutions for Class 9 Chapter 13

55 Qs

Related Questions to study

PQRS is a parallelogram. QM is the height from Q to SR and QN is the height from Q to PS. If SR=12cm and QM=7.6cm. Find QN, if PS=8cm.

1646450

EASY

Study later

View Answer

DF and BE are the height on sides AB and AD respectively in parallelogram ABCD. If the area of the parallelogram is 1470cm

2