# Sides AB and BC and median AD of a triangle ABC are respectively proportional to sides PQ and QR and median PM of ∆ PQR (see Fig. 6.41). Show that ∆ ABC ~ ∆ PQR

**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 criterion for two triangles.

In ΔABC and ΔPQR

AB/PQ = BC/QR = AD/PM [given]

AD and PM are median of ΔABC and ΔPQR respectively

⇒ BD/QM = (BC/2)/(QR/2) = BC/QR

Now In ΔABD and ΔPQM

AB/PQ = BD/QM = AD/PM

⇒ ΔABD ∼ ΔPQM

Now In ΔABC and ΔPQR

AB/PQ = BC/QR [given in the statement]

∠ABC = ∠PQR [∵ ΔABD ∼ ΔPQM]

⇒ ΔABC ∼ ΔPQR [SAS criteion]

**Video Solution:**

## Sides AB and BC and median AD of a triangle ABC are respectively proportional to sides PQ and QR and median PM of ∆ PQR (see Fig. 6.41). Show that ∆ ABC ~ ∆ PQR

### NCERT Class 10 Maths Solutions - Chapter 6 Exercise 6.3 Question 12:

Sides AB and BC and median AD of a triangle ABC are respectively proportional to sides PQ and QR and median PM of ∆ PQR (see Fig. 6.41). Show that ∆ ABC ~ ∆ PQR

In the above figure sides, AB and BC and median AD of a triangle ABC are respectively proportional to sides PQ, QR, and median PM of ∆PQR. Hence proved that ∆ABC ~ ∆ PQR