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If the two diagonals of a parallelogram ...

If the two diagonals of a parallelogram are equal than show it is a rectangle.

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Given: ABCD is a parallelogram in which AC=BD
To prove: parallelogram ABCD is a rectangle
Proof : In `triangleACB and triangleBDA`
AC=BD ( given )
AB=AB ( common )
BC=AD ( opposite sides of parallelogram )
`triangleABCcong triangleBDA`( by SSS)
`therefore` `angleABC=angleBAD`___1( by CPCT)
...
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RD SHARMA-QUADRILATERALS-All Questions
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  2. Diagonals necessarily bisect opposite angles in a rectangle(b) para...

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  3. If the two diagonals of a parallelogram are equal than show it is a re...

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  4. We get a rhombus by joining the mid-points of the sides of (a) par...

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  5. The bisectors of any two adjacent angles of a parallelogram intersec...

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  6. Show that the bisectors of angles of a parallelogram form a rectang...

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  7. The figure formed by joining the mid-points of the adjacent sides o...

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  8. The figure formed by joining the mid-points of the adjacent sides o...

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  9. Show that the quadrilateral formed by joining the mid-points of the ...

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  10. The figure formed by joining the mid-points of the adjacent sides o...

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  11. Show that the quadrilateral, formed by joining the mid-points of the ...

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  12. The figure formed by joining the mid-point of the adjacent sides of...

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  13. Find the measure of all the angles of a parallelogram, if one angle is...

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  14. In a parallelogram A B C D , if /D A B=75^@ and /D B C=60^@, then /B D...

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  15. In a parallelogram A B C D , if /D A B=75^@and /D B C=60^@, then /B D ...

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  16. A B C D is a parallelogram and E and F are the centroids of triangle...

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  17. A B C D is a parallelogram, M is the mid-point of B D and B M bisects ...

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  18. A B C D is a parallelogram and E is the mid-point of B C ,\ D E\ a n d...

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  19. If an angle of a parallelogram is two-third of its adjacent angle, f...

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  20. If the degree measures of the angles of quadrilateral are 4x ,\ 7x ...

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