Question

Prove that the angle bisectors of a parallelogram form a rectangle.

Explain with complete calculations & justifications.

Points : 20 ☺

Answer 1

see attachment I hope it will helps.....

Answer 2

Hi friend Here's the required answer:-
Given:- ABCD is a parellelogram, AP, BR, CP and BR are angle bisectors.
To prove:- PQRS is a rectangle.
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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