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Prove that in a quadrilateral the sum of...

Prove that in a quadrilateral the sum of all the sides is greater than the sum of its diagonals.

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To prove that in a quadrilateral the sum of all the sides is greater than the sum of its diagonals, we can follow these steps: ### Step-by-Step Solution: 1. **Draw the Quadrilateral**: Let’s denote the quadrilateral as ABCD, with diagonals AC and BD. 2. **Identify the Sides and Diagonals**: ...
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RD SHARMA ENGLISH-CONGRUENT TRIANGLE -All Questions
  1. Prove that the perimeter of a triangle is greater than the sum of i...

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  2. In A B C , side A B is produced to D so that B D=b cdot If /B=60^0 an...

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  3. Prove that in a quadrilateral the sum of all the sides is greater t...

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  4. In Figure, P Q R S is a quadrilateral in which diagonals P R and Q S i...

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  5. GIVEN : P Q R S is a quadrilateral. P Q is its longest side and R S ...

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  6. In Figure, A B and CD are respectively the smallest and longest side...

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  7. Of all the line segments drawn from a point P to a line m not containi...

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  8. In Figure, A D is a median and B L ,C M are perpendiculars drawn from ...

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  9. In Figure, B M and D N are both perpendiculars to the segments A C and...

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  10. If A B C is an isosceles triangle with A B=A C . Prove that the ...

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  11. If the altitudes from two vertices of a triangle to the opposite si...

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  12. A D and B C are equal perpendiculars to a line segment A B . Show that...

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  13. In A B C ,A B=A C , and the bisectors of angles B and C intersec...

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  14. In Figure, it is given that A B=E F ,B C=D E ,A B|B D and F E|C Edot P...

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  15. In Figure, it is given that A B=B C and A D=E C . Prove that A B E~=C ...

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  16. In Figure, l II m and M is the mid-point of the line segment A Bdot P...

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  17. In Figure, line l is the bisector of angle A and B is any point on l ....

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  18. In Figure, O is the mid point of A B and C D . Prove that (i) A O C~...

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  19. Prove that measure of each angle of an equilateral triangle is 60^0...

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  20. In Figure, it is given that A E=A D and B D=C Edot Prove that triangl...

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