Question

दर्शाइए कि एक समांतर चतुर्भुज के कोणों के समद्विभाजक एक आयत बनाते है।

Answer 1

Answer:

Given:- ABCD is a parellelogram, AP, BR, CP and BR are angle bisectors.

To prove:- PQRS is a rectangle.

Hu

Proof:- In Parellelogram ABCD, ADllCB

Therefore Angle A + Angle B=180°. [ Sum of Angles on the same the same side of transversal is 180°]

1/2 Angle A+ 1/2 Angle B=180°/2

1/2( Angle A + Angle B)=90° .....(1)

By Angle Sum Property in Triangle ASB,

Angle ABS + Angle BSA + Angle SAB= 180°

1/2 Angle B + Angle BSA + 1/2 Angle A= 180°( given that AP and BR are angle bisectors)

1/2( A+B) + Angle BSA=180°

90°+ Angle BSA =180° (From (1))

Angle BSA = 90°

Similarly , Angle BRC= CQD= APD =90°

Therefore a quadrilateral PQRS in which all angles are right angles is a rectangle

.'Proved'

Hope this helped u...

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