In a parallelogram ABCDABCD, the bisectors of AA and BB intersect at SS, BB and CC at RR, CC and DD at QQ and DD and AA at PP. What kind of a quadrilateral is PQRSPQRS?


Answer:

RectangleRectangle

Step by Step Explanation:
  1. The situation given in the question is represented by the figure below.
    A B D C P Q R S
  2. We are given that ABCDABCD is a parallelogram. DCABDCAB Also, as the adjacent angles of a parallelogram are supplementary, we have A+D=18012A+12D=90PAD+ADP=90APD=90[Sum of angles of a triangle is 180.]SPQ=90[Vertically opposite angles.] Similarly, PQR=90,QRS=90, and PSR=90.

    Thus, PQRS is a quadrilateral each of whose angles is 90.
    Hence, PQRS is a rectangle.

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