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Suppose line segments A B\ a n d\ C D in...

Suppose line segments `A B\ a n d\ C D` intersect at `O` in such a way that `A O=O D\ a n d\ O B=O C`. Prove that `A C=B D` but `A C` may not be parallel to `B D`.

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RD SHARMA ENGLISH-CONGRUENT TRIANGLE -All Questions
  1. In ΔABC a n d\ Δ P Q R ,\ A B=P Q ,\ B C=Q R\ a n d\ C B\ a n d\ R Q...

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  2. In Figure, X ,\ Y\ are two points on equal sides A B\ a n d\ A C o...

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  3. Suppose line segments A B\ a n d\ C D intersect at O in such a way tha...

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  4. If D is the mid-point of the hypotenuse A C of a right triangle A B...

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  5. A B is a line segment and line l is its perpendicular bisector. If ...

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  6. In quadrilateral A C B D ,\ A C=A D\ a n d\ A B\ bisects /A . Show th...

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  7. Prove that A B C is isosceles if any one of the following holds: A...

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  8. In Figure, P Q R S is a quadrilateral and T\ a n d\ U are respectively...

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  9. In Figure, P S=Q R\ a n d\ /S P Q=/R Q Pdot Prove that P Q S\ ~=\ Q...

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  10. In right triangle A B C , right angle at C ,\ M is the mid-point of th...

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  11. In Figure, A C=A E ,\ A B=A D\ a n d\ /B A D=/E A Cdot Prove that B C=...

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  12. In Figure, the side B A\ a n d\ C A have been produced such that B ...

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  13. In triangle P Q R , if P Q=R Q\ a n d\ L ,\ M\ a n d\ N are the mid-p...

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  14. In Figure, P Q R S is a square and S R T is an equilateral triangle...

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  15. Prove that the medians of an equilateral triangle are equal.

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  16. In a A B C , if /A=120^0a n d\ A B=A Cdot Find /B\ a n d\ /C

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  17. In A B C , if A B=A C\ a n d\ /B=70^0, find /A

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  18. The vertical angle of an isosceles triangle is 100^0dot Find its ba...

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  19. In Figure, A B=A C\ a n d\ /A C D=100^0, find /B A C

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  20. Find the measure of each exterior angle of an equilateral triangle.

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