Question

∠P ≅ ∠R seg PQ ≅ seg RQ
Prove that, △ PQT ≅ △ RQS.
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Answer 1

In ΔPQT and ΔRQS

∠P = ∠R …………[Given]

∠QPT = ∠QRS

PQ = RQ ………….[Given]

∠PQT = ∠RQS ………….[common]

∴ By ASA congruency

ΔPQT ≅ ΔRQS

Answer 2

Answer:

By ASA congruency, we can say that ∆PQR ≈ ∆RQS.

Step-by-step explanation:

Here, we are given that ∠ P ≈ ∠ R

Also, PQ ≈RQ.

To prove - ∆ PQT ≈ ∆RQS.

The congruency rule says that, there are 4 criteria of congruency -

1. When three sides are equal (SSS), the given triangle is congruent.

2. Two angles and a same corresponding side must be equal, so the given triangle will be congruent. (ASA)

3. Two sides must be equal and an angle included. (SAS)

4. Forth criteria is applicable for right-angled triangles, (RHS). Where a right angle, the hypotenuse and a corresponding side are equal.

In this figure angle Q is common for both the triangles.

∠P ≈∠ R. (Angle) [Given]

PQ ≈ RQ(side) [given]

∠Q ≈ ∠Q (common angle)

By ASA congruency, we can say that ∆PQR ≈ ∆RQS.