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If diagonal of a parallelogram bisects o...

If diagonal of a parallelogram bisects one of the angles of the parallelogram, it also bisects the second angle. Also, prove that it is a rhombus.

Text Solution

Verified by Experts

Given- AC diagonal bisects `/_A`
AB||CD and AC is transverse
`/_3=/_1-(1)`
AD||BC and AC is transverse
`/_2=/_4-(2)`
AC bisects`/_A`
`/_1=/_2-(3)`
`/_3=/_4`
...
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RD SHARMA-QUADRILATERALS-All Questions
  1. The diagonals of a parallelogram bisect each other.

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  2. The angle bisectors of a parallelogram form a rectangle.

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  3. If diagonal of a parallelogram bisects one of the angles of the par...

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

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  5. The diagonals of a quadrilateral A B C D are perpendicular. Show that ...

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  6. ABCD is a rhombus and P ,Q ,R ,S are the mid-points of A B ,B C ,C D ,...

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

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  8. Prove that the figure formed by joining the mid-points of the pair of ...

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  9. In Figure, A D is the median and D E A Bdot Prove that B E is the med...

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  10. In a A B C , find the measures of the angles of the triangle formed b...

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  11. In A B C ,A D is the median through A and E is the mid-point of A D ....

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  12. In Figure, A D , and B E are medians of A B C and B E || D Fdot Prove...

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  13. P ,Q and R are, respectively, the mid-points of sides B C ,C A and A B...

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  14. P is the mid-point of side A B of a parallelogram A B C D . A Line thr...

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  15. In Figure, A B C D isa trapezium in which side A B is a parallel to si...

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  16. In Figure, A B C D is a parallelogram. E and F are the mid-points of t...

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  17. A B C D is a parallelogram. P is a point on A D such that A P=1/3A D a...

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  18. In a A B C ,\ B M\ a n d\ C N are perpendiculars from B\ a n d\ C r...

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  19. In triangle ABC, M ,N and P are the mid-points of A B ,A C and B C res...

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  20. Prove that the line segment joining the mid-points of the diagonals of...

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