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E , F , G , H are respectively, the mid...

`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`

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RD SHARMA ENGLISH-AREA OF PARALLELOGRAMS AND TRIANGLES-All Questions
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  2. X Y is a line parallel to side B C of triangle A B C . If B E II AC a...

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  3. E , F , G , H are respectively, the mid-points of the sides A B ,B C ...

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  4. X Y is a line parallel to side B C of /\ A B C. B E || AC and C F || A...

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  5. E , F , G , H are respectively, the mid-points of the sides A B ,B C ,...

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  6. The side A B of a parallelogram A B C D is produced to any point Pdot ...

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  7. Any point D is taken in the base B C of a triangle A B C\ a n d\ A...

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  8. In A B C ,D is the mid-point of A B ,P is any point of B CdotC Q P D...

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  9. In a parallelogram A B C D ,E ,F are any two points on the sides A B a...

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  10. In Figure, A B C D is a trapezium in which A B||D C .\ \ D C is prod...

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  11. Prove that the area of an equilateral triangle is equal to (sqrt(3))...

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  12. In Figure, B C || X Y ,\ B X || C A and A B || Y C. Prove that: a r( A...

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  13. In Figure, A B C D is a parallelogram. Prove that: a r( B C P)=a r( D ...

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  14. A B C is a triangle in which D is the mid-point of BC and E is the mid...

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  15. A B C D is a parallelogram X and Y are the mid-points of B C and C D r...

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  16. The diagonals of a parallelogram A B C D intersect at a point O. T...

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  17. The medians B E\ a n d\ C F of a triangle A B C intersect at G. ...

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  18. In Figure, compute the area of quadrilateral A B C D.

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  19. In Figure, P Q R S is a square and T\ a n d\ U are, respectively, ...

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  20. Compute the area of trapezium P Q R S in the given figure.

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