9th Class
Mathematics
Quadrilaterals
Question Bank
Quadrilaterals
question_answer
\[APB\] and \[CQD\] are parallel lines and a transversal \[PQ\] cuts them at \[P\] and\[Q\]. Which of the following is formed by the bisectors of angles \[APQ,\,\,BPQ,\,\,CQP\] and\[PQD\]?
A) A rectangle
B) A rhombus
C) A square
D) Any other parallelogram
Correct Answer:
A
Solution :
\[\angle APQ+\angle CQP={{180}^{o}}\] \[\Rightarrow \]\[\frac{\angle APQ}{2}+\frac{\angle CQP}{2}{{90}^{o}}\] \[\Rightarrow \]\[\angle RPQ+\angle PQR={{90}^{o}}\] \[\Rightarrow \]\[\Delta PQR\]is a right angled triangle Similarly, \[\Delta PQR\]is a right angled triangle \[\Rightarrow \]\[PQRS\]is rectangle.