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A B is a line segment, A X and B Y are t...

`A B` is a line segment, `A X` and `B Y` are two equal line segments drawn on opposite sides of line `A B` such that `A X B Ydot` If `A B` and `X Y` intersect each other `P ,` prove that `A P XcongB P Y` `A B` and `X Y` bisect each other.

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in `/_\APX` and`/_\BPY`
`AP=BP`(given AB and XY bisect each other)
`/_APX=/_BPY`(vertically opposite angle)
`XP=YP`(given AB and XY bisect each other)
from SAS theorem`/_\APXcong/_\BPY`
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RD SHARMA-CONGRUENT TRIANGLE -All Questions
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  2. In triangle A B C ,/B=45^@,/C=55^@ and bisector of /A meets B C at a p...

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  3. A B is a line segment, A X and B Y are two equal line segments drawn o...

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  4. In Figure, if A B D E ,/B A C=35^0 and /C D E=53^0 , find /D C Edot

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  5. l and m are two parallel lines intersected by another pair of parall...

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  7. Two triangles are congruent if two angles and the included side of o...

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  8. A ,B ,C , are three angles of a triangle. If A-B=15^@,B-C=30^@, find /...

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  9. In Figure, diagonal A C of a quadrilateral A B C D bisects the angle...

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  10. In a triangle A B C ,/A B C=/A C B and the bisectors of /A B C and /A ...

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  11. In Figure, /B C D=/A D C and /A C B=/B D Adot Prove that A D=B C and /...

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  12. If each angle of a triangle is less than the sum of the other two, s...

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  13. In two right triangles, one side and an acute angle of one triangle ...

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  14. If Figure, if Q T|P R ,/T Q R=40^0 AND /S P R=30^0, find x and ydot F...

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  15. If D is any point on the base B C produced, of an isosceles triangle A...

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  16. In figure, sides Q P and R Q of P Q R are produced to point S and T re...

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  17. Show that in a right triangle the hypotenuse is the longest side. G...

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  18. An exterior angle of a triangle is 110^0 , and one of the interior opp...

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  19. Show that the sum of the three altitudes of a triangle is less than...

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  20. The sides B C ,C A and A B of a triangle A B C , are produced in or...

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