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Show that the diagonals of a rhombus are perpendicular to each other

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Using analytical geometry, prove that the diagonals of a rhombus are perpendicular to each other.

Using analytical geometry, prove that the diagonals of a rhombus are perpendicular to each other.

Diagonals of a rhombus are equal.

Statement-l: If the diagonals of the quadrilateral formed by the lines px+ gy+ r= 0, p'x +gy +r'= 0, p'x +q'y +r'= 0 , are at right angles, then p^2 +q^2= p^2+q^2 . Statement-2: Diagonals of a rhombus are bisected and perpendicular to each other.

In a quadrilateral ABCD, it is given that AB |\|CD and the diagonals AC and BD are perpendicular to each other. Show that AD.BC >= AB. CD .

The diagonals of a rhombus are perpendicular. The contrapositive of the above statement is

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

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

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RD SHARMA ENGLISH-QUADRILATERALS-All Questions
  1. In Figure, A B C D is a trapezium in which A B ll C D and A D=B Cdot s...

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  2. If the diagonals of a parallelogram are perpendicular, then it is a ...

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  3. Show that the diagonals of a rhombus are perpendicular to each othe...

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  4. If the diagonals of a parallelogram are equal and intersect at right ...

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

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  6. The diagonals of a rectangle A B C D meet at Odot If /B O C=44^0, find...

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  7. P Q R S is a square. P R and S Q intersect at Odot State the measure o...

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  8. ABCD is a rectangle in which diagonal AC bisects /A as well as /C ....

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  9. A B C D is a rhombus with /A B C=56^0dot Determine /A C Ddot

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  10. Each of the four angles of a rectangle is a right angle.

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  11. Each of the four sides of a rhombus is of the same length.

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

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  13. If A B C and D E F are two triangles such that A B ,B C are respe...

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  14. In Figure, A B C D is a parallelogram and X\ a n d\ Y are points on th...

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  15. In Figure, A B C is an isosceles triangle in which A B=A Cdot and C P|...

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  16. In Figure, X ,Y are the mid-points of opposite sides A B and D C of a ...

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

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

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

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

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