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A B ,C D are two parallel lines and a tr...

`A B ,C D` are two parallel lines and a transversal `l` intersects `A B` at `X` and `C D` at `Y` Prove that the bisectors of the interior angles form a parallelogram, with all its angles right angles i.e., it is a rectangle.

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TO prove= PXQY is a recctangle
Proof-
AB||CD
`/_AXY=/_DYX`
`1/2/_AXY=1/2/_DYX`
`/_1=/_2`
XY intersect PX and QY at XY
`/_1=/_2`
...
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RD SHARMA-QUADRILATERALS-All Questions
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  2. Each of the four sides of a rhombus is of the same length.

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  3. A B ,C D are two parallel lines and a transversal l intersects A B at ...

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  4. If A B C and D E F are two triangles such that A B ,B C are respecti...

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  5. In Figure, A B C D is a parallelogram and X and Y are points on the ...

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  6. In Figure, A B C is an isosceles triangle in which A B=AC. CP parellel...

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  8. Two segments A C and B D bisect each other at O . Prove that A B C D i...

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  9. Each of the angles of a square is a right angle and each of the four ...

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  10. The diagonals of a rectangle are of equal length.

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  11. If the diagonals of a quadrilateral bisect each other, then the qua...

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  12. A quadrilateral is parallelogram if its opposite angles are equal.

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  13. A quadrilateral is a parallelogram if its opposite sides are equal.

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  14. In Figure, A B C D is a parallelogram in which /A=60^0 . If the bisect...

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  15. In figure, Show that if the diagonals of a quadrilateral are equal and...

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  16. Show that the diagonals of a square are equal and bisect each other at...

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  17. Show that if the diagonals of a quadrilateral bisect each other at r...

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  18. A quadrilateral is a parallelogram, if its one pair of opposite sides ...

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  20. In a triangle A B C median A D is produced to X such that A D=D Xdot P...

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