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A B C D is a square, X\ a n d\ Y are poi...

`A B C D` is a square, `X\ a n d\ Y` are points on sides `A D\ a n d\ B C` respectively such that `A Y=B X` . Prove that `B Y=A X\ a n d\ /_B A Y=/_A B X`

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To prove that \( BY = AX \) and \( \angle BAY = \angle ABX \), we will use the properties of congruent triangles. ### Step-by-Step Solution: 1. **Identify the Given Information**: - Let \( ABCD \) be a square. - Points \( X \) and \( Y \) are on sides \( AD \) and \( BC \) respectively. - It is given that \( AY = BX \). ...
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RD SHARMA-CONGRUENT TRIANGLE -All Questions
  1. In perpendiculars from any point within an angle on its arms are con...

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  2. In Figure, A D\ |C D\ and C B\ |c ddot If A Q=B P\ a n d\ D P=C Q , p...

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  3. A B C D is a square, X\ a n d\ Y are points on sides A D\ a n d\ B C r...

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  4. Which of the following statements are true (T) and which are false (...

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  5. Fill the blanks in the following so that each of the following stateme...

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  6. In a A B C ,\ if /A=45^0\ a n d\ /B=70^0dot Determine the shortest ...

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  7. In a A B C , if /A=50^0\ a n d\ /B=60^0 , determine the shortest a...

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  8. In Figure, P Q > P RdotQ S\ a n d\ R S are the bisectors of L Q and /R...

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  9. In Figure, sides L M\ a n d\ L N OF LMN are extended to P\ a n d\ Q r...

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  10. In Figure, P Q=P Rdot Show that P S > P Q

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  11. In Figure, A B > A Cdot Show that A B > A D

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  12. If D is any point on the base B C produced, of an isosceles tria...

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  13. In Figure, if A D is the bisector of L A , show that: A B > B D (ii) ...

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  14. Show that in a right angled triangle, the hypotenuse is the longest...

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  15. In Figure, A C > A B and A D is the bisector of L A . Show that A D C ...

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

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  17. Prove that any two sides of a triangle are together greater than twi...

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  18. Prove that the perimeter of a triangle is greater than the sum of it...

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  19. Show that the difference of any two sides of a triangle is less than...

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  20. In Figure, P Q R is a triangle and S is any point in its interior, s...

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