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4. The vertices of a parallelogram lie on a circle. Prove that its diagonals are equal.
Asked by avantikadandapani | 17 Nov, 2014, 06:47: PM
answered-by-expert Expert Answer
G i v e n space t h a t space t h e space v e r t i c e s space o f space a space p a r a l l e log r a m space l i e space o n space a space c i r c l e. T h a t space i s space i t space i s space a space c y c l i c space p a r a l l e log r a m space a n d space h e n c e space t h e space o p p o s i t e space a n g l e s space a r e space s u p p l e m e n t a r y. I n space a space p a r a l l e log r a m comma space o p p o s i t e space a n g l e s space a r e space e q u a l space a n d space a d j a c e n t space a n g l e s space a r e space s u p p l e m e n t a r y. L e t space x space a n d space y space b e space t h e space a d j a c e n t space a n g l e s space o f space t h e space p a r a l l e log r a m S i n c e space i t space i s space c y c l i c comma space w e space h a v e comma x plus x equals 180 degree rightwards double arrow 2 x equals 180 degree rightwards double arrow x equals fraction numerator 180 degree over denominator 2 end fraction equals 90 degree I n space a space p a r a l l e log r a m comma space i f space o n e space o f space t h e space a n g l e space i s space 90 degree comma space t h e n space i t space i s space a space r e c tan g l e. I n space a space r e c tan g l e comma space d i a g o n a l s space a r e space e q u a l space a n d space h e n c e space p r o v e d.
Answered by Vimala Ramamurthy | 18 Nov, 2014, 08:45: AM

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CBSE 9 - Maths
if the diagonals of a parallelogram are equal then show that it is a rectangle
Asked by priyankaubelal | 05 Mar, 2020, 10:25: PM
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CBSE 9 - Maths
If an angle of a parallelogram is two thirds of its adjacent angle find the angle of a parallelogram .
Asked by agarwalsenterprises | 19 Feb, 2020, 07:08: PM
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CBSE 9 - Maths
In the figure ABCD is a parallelogram in which DAB = 80o and DBC = 60o. Calculate CDB and ADB.
Asked by Topperlearning User | 09 Dec, 2013, 01:37: AM
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CBSE 9 - Maths
Find the measure of each angle of a parallelogram, if one of its angles is 30o less than twice the smallest angle.
Asked by Topperlearning User | 04 Jun, 2014, 01:23: PM
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CBSE 9 - Maths
In the given figure, PN and RM are perpendiculars to the diagonal QS of a parallelogram PQRS. Prove that PNS RMQ and PN = RM.
Asked by Topperlearning User | 04 Jun, 2014, 01:23: PM
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CBSE 9 - Maths
ABCD is a parallelogram in which X and Y are the mid points of AB and DC respectively. If AY and DX intersect in P while CX and BY intersect in Q, show that quadrilateral PXQY is a parallelogram.
Asked by Topperlearning User | 09 Dec, 2013, 02:35: AM
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CBSE 9 - Maths
LMNO is a parallelogram. Compute the values of x and y.
Asked by Topperlearning User | 09 Dec, 2013, 01:39: AM
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CBSE 9 - Maths
Characterize the following statements a TRUE or FALSE and give reason for your answer. If a pair of adjacent sides of a parallelogram is equal, it must be a rhombus or a square.
Asked by Topperlearning User | 04 Jun, 2014, 01:23: PM
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CBSE 9 - Maths
In a parallelogram ABCD, prove that the sum of any two consecutive angles is 180o.
Asked by Topperlearning User | 09 Dec, 2013, 01:40: AM
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CBSE 9 - Maths
In a ABC median AD is produced to X such that AD = DX. Prove that ABXC is a parallelogram.         
Asked by Topperlearning User | 04 Jun, 2014, 01:23: PM
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