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CBSE Class 9 Answered

Show that bisectors of angles of a parallelogram form a rectangle.
Asked by Topperlearning User | 04 Jun, 2014, 01:23: PM
answered-by-expert Expert Answer

P, Q, R and S are the points of intersection of bisectors of the angles of the parallelogram.

In ADS,

DAS + ADS =

(A and D are interior angles on the same side of the transversal)

Also in ADS,

DAS + ADS + DSA = 180o (angle sum property)

Similarly, it can be shown that APB or SPQ = 90o

Also, SRQ = RQP = 90o

Hence, PQRS is a rectangle.

Answered by | 04 Jun, 2014, 03:23: PM

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