Question

in fig ps = pr and angle tps=angle QPR prove that pt =pq

Answer 1

Hope that this answer will help you

Answer 2

PT = PQ due to the congruency of ΔPST and ΔPRQ

Given

• Figure
• PS = PR

• ∠ TPS = ∠ QPR

To Find

Proof of PT = PQ

Solution

Here we have ΔPSR

Here PS = PR

Therefore, ΔPSR is an isosceles triangle.

Therefore,

∠PSR = ∠PRS (angle made by the equal sides on the base is always equal)

Hence

180° - ∠PSR = 180° - ∠PRS

or, ∠PST = ∠ PRQ                      [1]

Now in ΔPST and ΔPRQ

∠ TPS = ∠ QPR     (Given)

PS = PR                 (Given)

∠PST = ∠ PRQ      (equation [1])

Therefore,

ΔPST ≅ ΔPRQ [ASA congruency criteria]

Therefore,

PT = PQ     (c.p.c.t)

Here,

ASA means Angle Side Angle, which is when two angles and their corresponding sides in 2 triangles are equal.

c.p.c.t = congruent parts of conguent triangles.

Hence proved that PT = PQ due to the congruency of ΔPST and ΔPRQ

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