Question

In triangle pqr the line segment PS is the angle bisector of angle p then PR÷SR=QS÷PQ . Is it true or false

Answer 1

Answer:

u should know the answer

Step-by-step explanation:

Answer 2

Answer:

True

Step-by-step explanation:

In the given figure,

Draw RX parallel to PS to meet QP produced at X

Let angle QPS = angle 1, angleSPR = angle2, anglePXR = angle, anglePRX = angle3.

Angle2 = angle3. (alternate angle)

Angle = angle4. (corresponding angle)

But, angle1 = angle2. (since PS is angle bisector)

Therefore, angle3 = angle4 => PX = PR

Now, in ∆QRX,we have RX parallel to PS.

=> QS/QP = SR/PX

=> QS/SR = QP/PX => QS/SR =PQ/PR. (since,PR=PX proved above)

Hence,QS/SR = PQ/PR

Thus , QS ÷ PQ = PR ÷ SR

So,

PR ÷ SR = QS ÷ PQ

Hence, proved.