Question

In ΔPQR the sides QP and RP have been produced to S and T such that PQ = PS and PR = PT. Prove that the segment QR || ST.

Answer 1

Hello, here is your answer.

Hope it helps you.

Answer 2

Answer:

Proved that QR || ST

Step-by-step explanation:

Given a triangle PQR.

The sides QP and RP are extended to S and T, as shown in the figure.    

And the measures, PQ = PS and PR = PT  

The lines RT and SQ are the intersecting lines.

In intersecting lines, the vertically opposite angles are equal.

Therefore, $\angle TPS = \angle QPR$

Applying the Side-Angle-Side(SAS) rule, two triangles are said to be congruent when two sides and an included angle of two triangles are equal.

We get, $\triangle TPS \cong \triangle QPR$

Applying the corresponding parts of congruent triangles (CPCT) rule, if two triangles are congruent, then all their corresponding angles and sides are equal.

Thus $\angle PTS = \angle PRQ$ and $\angle TSP = \angle PQR$

Thus the angles represent the alternate interior angles and hence they are equal.

Therefore, the line QR must be parallel to the line ST.

Hence proved that  QR || ST

For more problems:

https://brainly.in/question/27622697

https://brainly.in/question/6839681