Home
Class 9
MATHS
If E ,F ,G and H are respectively the mi...

If `E ,F ,G` and `H` are respectively the mid-points of the sides of a parallelogram `A B C D ,` show that `a r(E F G H)=1/2a r(A B C D)dot`

Text Solution

Verified by Experts

Let us join HF.
In parallelogram ABCD,
`AD = BC` and `AD || BC `(Opposite sides of a parallelogram are equal and parallel)
`AB = CD` (Opposite sides of a parallelogram are equal)
...
Promotional Banner

Similar Questions

Explore conceptually related problems

If E,F,G and H are respectively the mid- points of the sides of a parallelogram ABCD , show that ar(EFGH)=(1)/(2) ar (ABCD)

If E,F,G and H are respectively the mid- points of the sides of a parallelogram ABCD , Show that ar(EFGH)=(1)/(2)AR(ABCD)

E , F , G , H are respectively, the mid-points of the sides A B ,B C ,C D and D A of parallelogram A B C D . Show that the quadrilateral E F G H is a parallelogram and that its area is half the area of the parallelogram, A B C Ddot GIVEN : A quadrilateral A B C D in which L ,F ,G ,H are respectively the mid-points of the sides A B ,B C ,C D and D Adot TO PROVE : (i) Quadrilateral E F G H is a parallelogram a r(^(gm)E F G H)=1/2a r(^(gm)A B C D) CONSTRUCTION : Join A C and H F

D,E and F are respectively the mid-points of the sides BC,CA and AB of a /_ABC. Show that (i) BDEF is a parallelogram

D, E and F are respectively the mid-points of the sides BC, CA and AB of aDeltaA B C . Show that (i) BDEF is a parallelogram. (ii) a r" "(D E F)=1/4a r" "(A B C) (iii) a r" "(B D E F)=1/2a r" "(A B C)

p A N D q are any two points lying on the sides D C a n d A D respectively of a parallelogram A B C Ddot Show that a r( A P B)=a r ( B Q C)dot

In A A B C ,\ P\ a n d\ Q are respectively the mid-points of A B\ a n d\ B C and R is the mid-point of A Pdot Prove that: a r\ (\ P R Q)=1/2a r\ (\ A R C)

In a parallelogram A B C D ,E ,F are any two points on the sides A B and B C respectively. Show that a r( A D F)=a r( D C E)dot

D ,\ E ,\ F are the mid-points of the sides B C ,\ C A and A B respectively of a A B C . Determine the ratio of the areas of D E F and A B C .

In Fig. 4.103, C D and G H are respectively the medians of A B C and E F G . If A B C ~ F E G , prove that (FIGURE) A D C ~ F H G (ii) (C D)/(G H)=(A B)/(F E) (iii) C D B ~ G H E