In a parallelogram ABCD, the bisectors of ∠A and ∠B intersect at S, ∠B and ∠C at R, ∠C and ∠D at Q and ∠D and ∠A at P. What kind of a quadrilateral is PQRS?
Answer:
Rectangle
- The situation given in the question is represented by the figure below.
- We are given that ABCD is a parallelogram.
⟹DC∥AB
Also, as the adjacent angles of a parallelogram are supplementary, we have
Similarly, and .
Thus, is a quadrilateral each of whose angles is .
Hence, is a .