Question

Each angle of a rectangle is bisected. Let P,Q,R and S be the points of intersection of the pairs of bisectors adjacent to the same side of the rectangle. Then PQRS is a

Answer 1

Answer:

ANSWER

ABCD is a given rectangle.

AS , DS , BQ, CQ is angle bisector of angle A, angle D, angle B, angle C respectively.

In triangle ASD

Angle DAS= ADS =45 degree

So angle ASD =180-(45+45) = 90 degree

angle RSP = angle ASD =90 degree (vertically opposite angle )

Similarly for triangle BQC

angle QBC = angle BCQ = 45 degrees.

Hence, angle BQC = 180-(45+45) = 90 degree.

angle BQC = angle RQP = 90 degree ( vertically opposite angle )

Now, since AB is parallel to CD and DR and PB are angle bisectors so DR becomes parallel to PB. And angle RSP = angle RQP = 90 degree.

So, PS becomes parallel to QR.

This proves that PQRS is a rectangle.

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Answer 2

Answer:

His answer is correct

Step-by-step explanation: