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

`E , F , G , H` are respectively, the mid-points of the sides of parallelogram `A B C D` . Show that the area of EFGH 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 : `a r(^(gm)E F G H)=1/2a r(^(gm)A B C D)` CONSTRUCTION : Join `H` and `F`

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EF||AC and `EF=1/2AC-(1)`
In`/_ADC`, GH||AC and `GH=1/2AC-(2)`
EF=GH and EF||GH
EFGH is an parallelogram
ABCD is a parallelogram
AD=BC,AD||BC.
`1/2AD=1/2BC`
HD=FC,HD||FC
...
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RD SHARMA ENGLISH-AREA OF PARALLELOGRAMS AND TRIANGLES-All Questions
  1. In Figure, P Q R S and A B R S are parallelograms and X is any point o...

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  2. The diagonals of a parallelogram A B C D intersect at a point Odot Thr...

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  3. E , F , G , H are respectively, the mid-points of the sides of parall...

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

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

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  6. The medians B E and C F of a triangle A B C intersect at G . Prove tha...

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  7. ABCD is a parallelogram. E is a point on BA such that BE =2 EA and F i...

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  8. A circular grassy plot of land, 42 m in diameter has a path of 3.5m wi...

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  9. A point O inside a rectangle A B C D is joined to the vertices. Prove ...

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  10. Which of the following figure lie on the same base and between the ...

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  11. A B C D is a quadrilateral and B D is one of its diagonals as shown...

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  12. In parallelogram A B C D ,A B=10c mdot The altitudes corresponding to ...

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  13. Show that the segment joining the mid-points of a pair of opposite ...

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  14. The diagonals of a parallelogram A B C D intersect at O. A line ...

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  15. Prove that of all parallelograms of which the sides are given, the ...

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  16. In Figure, A B C D is a parallelogram and E F C D is a rectangle. Al...

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  17. If E ,\ F ,\ G\ a n d\ H are respectively the mid-points of the side...

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  18. p\ A N D\ q are any two points lying on the sides D C\ a n d\ A D r...

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  19. In Figure, P is a point in the interior of a parallelogram A B C Dd...

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  20. In Figure, A B C D is a parallelogram, A E\ |D C\ a n d\ CC F|A D . ...

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