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A point `O` inside a rectangle `A B C D` is joined to the vertices. Prove that the sum of the areas of a pair of opposite triangles so formed is equal to the sum of the other pair of triangles. Given: A rectangle `A B C D\ a n d\ O` is a point inside it. `O A ,\ O B ,\ O C\ a n d\ O D` have been joined. To Prove: `a r\ (A O D)+\ a r\ ( B O C)=\ a r\ ( A O B)+\ a r( C O D)`

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RD SHARMA ENGLISH-AREA OF PARALLELOGRAMS AND TRIANGLES-All Questions
  1. Diagonals A C and B D of a quadrilateral A B C D intersect at O in suc...

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  2. In Figure, diagonals AC and BD of quadrilateral ABCD intersect at O ...

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  3. A point O inside a rectangle A B C D is joined to the vertices. Prov...

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  4. Show that the area of a rhombus is half the product of the lengths ...

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  5. A B C D is a parallelogram and O is any point in its interior. Prove t...

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  6. A quadrilateral A B C D is such that diagonal B D divides its area in ...

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  7. Parallelogram A B C D and rectangle A B E F have the same base A B and...

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  8. O is any point on the diagonal B D of the parallelogram A B C D. Prove...

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  9. Triangles A B C and DBC are on the same base B C with A, D on opposite...

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  10. D and E are points on sides AB and AC respectively of DeltaA B Csuch...

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  11. If the medians of a triangle A B C intersect at G , show that a r( tr...

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  12. D, E and F are respectively the mid-points of the sides BC, CA and AB...

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  13. B D is one of the diagonals of a quadrilateral A B C D. A M and C N ...

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  14. A B C D is a quadrilateral. A line through D , parallel to A C , mee...

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  15. If the median of a △ABC intersect at G. show that ar (△AGC) = ar (△AGB...

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

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

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

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