Question

Good afternoon everyone

in the figure,,
QR/QS = QT/PR And angle 1 =angle 2
then prove That PQS similar to TQR...



is the above solution correct or not?
if not,, then please provide the correct solution...

Answer 1

Step-by-step explanation:

Please find the answer to your question below

Here you didnot provide any diagram for the question

But if in two triangles if the sides are proportional and one angle is equal then the triangles are similar according to SAS criterion

So Given thatIn triangle TQR, QR/QS = QT/PR and angle 1 = angle 2.

So triangle PQS ~ triangle PQR.

Answer 2

Given,

QR/QS = QT/PR... (1)

Angle(1) = Angle(2)....(2)

We know,

Identify (SAS) is used when we deal with proving side, angle, side equal for both the triangles,

We have,

In triangle(PQR),

Angle(1) = Angle(2)...[given]

So,

We know sides opposite to equal angles are equal,

Then,

PR = PQ.... (3)

From (1) and (3),

QR/QS = QT/PQ... (4)

Now, in triangle(PQS) and triangle(TQR),

From (4),

QR/QS = QT/PQ

And angle(1) = Angle(1)...[common angle]

Hence proved by SAS congruence identity,

Triangle (PQS) ~ Triangle (TQR)