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ABCD is a rectangle in which diagonal...

ABCD is a rectangle in which diagonal AC bisects `/_A` as well as `/_C` . Show that: (i) ABCD is a square (ii) diagonal BD bisects `/_B` as well as `/_Ddot` .

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`PQRS` is a square .
`PR = SQ` (given )
`O` is common .
`POQ=QOR `....(i)
`POQ+QOR=180°`
From equation (i) we have already see that `POQ =QOR` .
`POQ+QOR=180°`
`POQ+POQ=180°`
`2POQ=180°`
`POQ=(180°)/2`
`POQ=90°`
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RD SHARMA-QUADRILATERALS-All Questions
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  2. P Q R S is a square. P R and S Q intersect at Odot State the measure o...

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

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

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

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

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

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

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

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  16. A quadrilateral is parallelogram if its opposite angles are equal.

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  17. A quadrilateral is a parallelogram if its opposite sides are equal.

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  18. In Figure, A B C D is a parallelogram in which /A=60^0 . If the bisect...

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  19. In figure, Show that if the diagonals of a quadrilateral are equal and...

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

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