# In Fig. 6.36 QR/QS = QT/PR and ∠1 = ∠2. Show that ΔPQS ~ ΔTQR

**Solution:**

As we know if one angle of a triangle is equal to one angle of the other triangle and the sides including these angles are proportional, then the two triangles are similar.

This is referred to as SAS (Side - Angle - Side) similarity criterion for two triangles.

In ΔPQR

∠1 = ∠2

⇒ PR = PQ (In a triangle sides opposite to equal angles are equal)

In ΔPQS and ΔTQR

∠PQS = ∠TQR = ∠1 (same angle)

QR/QS = QT/PQ (PR = PQ)

⇒ ΔPQS ~ ΔTQR (SAS criterion)

**Video Solution:**

## In Fig. 6.36 QR/QS = QT/PR and ∠1 = ∠2. Show that ΔPQS ~ ΔTQR.

### NCERT Class 10 Maths Solutions - Chapter 6 Exercise 6.3 Question 4:

In Fig. 6.36 QR/QS = QT/PR and ∠1 = ∠2. Show that ΔPQS ~ ΔTQR.

Hence it is proved that triangle PQS is similar to triangle TQR.