Q8 of 109 Page 287

If is a point within a quadrilateral show that

Given: In ABCD, O is any point within the quadrilateral.
To prove:
Proof:


We know that the sum of any two sides of a triangle is greater than the third side.
So, in ∆AOC,


OA + OC > AC …(1)


Also, in ∆ BOD,


OB + OD > BD …(2)


Adding 1 and 2, we get,


(OA + OC) + (OB + OD) > (AC + BD)
∴ OA + OB + OC + OD > AC + BD


Hence proved.


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(i) bisects and


(ii)


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7

In the given figure, ABCD is a square and If PB = QC = DR, prove that

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In the adjoining figure, is a quadrilateral and is one of its diagonals. Prove that:

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(ii)


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10

Prove that the sum of all the angles of a quadrilateral is 360°.