Register
Register

Q. 74.4( 9 Votes )

In the given figu

Answer :

Given that ∆PQR and ∆SQR lie on the same side of the common base QR

Also, ∆PQR and ∆SQR are isosceles triangles .


So, QS=RS and QP=RP…………(1)


To prove : SP is the perpendicular bisector of line QR


Proof : In ∆PQS and ∆PRS,


QS=RS (given)


QP=RP (given)


SP=SP (common)


∆PQS ∆PRS (by SSS rule)


So, PSQ=PSR (by cpct)…………….(2)


Now, in ∆QSO and ∆RSO,


QS=RS (given)


SO=SO (common)


PSQ=PSR (from (2))


∆QSO ∆RSO (by SAS rule)


So, QO=RO (by cpct)


And QOS=ROS (by cpct)………..(3)


Now, QOS+ROS=180° (straight angle)


QOS+QOS=180° (from (3))


2QOS =180°


QOS=90°


Hence, SO is the perpendicular bisector of QR


So, SP is also the perpendicular bisector of QR


Rate this question :

How useful is this solution?
We strive to provide quality solutions. Please rate us to serve you better.
Try our Mini CourseMaster Important Topics in 7 DaysLearn from IITians, NITians, Doctors & Academic Experts
Dedicated counsellor for each student
24X7 Doubt Resolution
Daily Report Card
Detailed Performance Evaluation
caricature
view all courses
RELATED QUESTIONS :

In the given figuRajasthan Board Mathematics

In the given figuRajasthan Board Mathematics

Prove that the trRajasthan Board Mathematics