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CBSE Class 9 Answered

Show that the bisectors of angles of a parallelogram form a rectangle.
Asked by pkirankumar4321 | 23 Feb, 2015, 09:21: PM
answered-by-expert Expert Answer
C o n s i d e r space t h e space f o l l o w i n g space f i g u r e.
G i v e n space t h a t space A B C D space i s space a space p a r a l l e log r a m. L e t space A G comma space B H comma space C E space a n d space D F space b e space t h e space a n g l e space b i s e c t o r s space o f space angle A comma angle B comma angle C space a n d space angle D space r e s p e c t i v e l y. W e space n e e d space t o space p r o v e space t h a t space I J K L space i s space a space r e c tan g l e. S i n c e space A B C D space i s space a space p a r a l l e log r a m comma space angle A equals angle C space a n d space angle B equals angle D A l s o space angle A plus angle D equals 180 degree space comma space angle C plus angle D equals 180 degree comma space angle B plus angle C equals 180 degree space a n d space angle A plus angle B equals 180 degree S i n c e 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 comma space w e space h a v e comma angle B A D plus angle A B C equals 180 degree rightwards double arrow fraction numerator angle B A D over denominator 2 end fraction plus fraction numerator angle A B C over denominator 2 end fraction equals fraction numerator 180 degree over denominator 2 end fraction rightwards double arrow angle B A J plus angle A B J equals 90 degree S i m i l a r l y comma space angle A B C plus angle B C D equals 180 degree rightwards double arrow fraction numerator angle A B C over denominator 2 end fraction plus fraction numerator angle B C D over denominator 2 end fraction equals fraction numerator 180 degree over denominator 2 end fraction rightwards double arrow angle C B J plus angle B C K equals 90 degree A n d comma angle B C D plus angle C D A equals 180 degree rightwards double arrow fraction numerator angle B C D over denominator 2 end fraction plus fraction numerator angle C D A over denominator 2 end fraction equals fraction numerator 180 degree over denominator 2 end fraction rightwards double arrow angle D C L plus angle C D L equals 90 degree A l s o comma angle C D A plus angle B A D equals 180 degree rightwards double arrow fraction numerator angle C D A over denominator 2 end fraction plus fraction numerator angle B A D over denominator 2 end fraction equals fraction numerator 180 degree over denominator 2 end fraction rightwards double arrow angle A D L plus angle I A D equals 90 degree T h u s comma space t h e space p a r a l l e log r a m space i s space a space r e c tan g l e
Answered by Vimala Ramamurthy | 24 Feb, 2015, 11:22: 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
ANSWERED BY EXPERT ANSWERED BY EXPERT
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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