NCERT Class 10 Mathematics

TRIANGLES 135

Now, PQ || EF and ABC ✁ DPQ (How ?)

So, ✂ A = ✂ D,✂ B = ✂ P and ✂ C = ✂ Q

Therefore, ABC ~ DEF (Why?)

We now take some examples to illustrate the use of these criteria.

Example 4 : In Fig. 6.29, if PQ || RS, prove that POQ ~ SOR.

Fig. 6.29

Solution : PQ || RS (Given)

So, ✂ P =✂ S (Alternate angles)

and ✂ Q =✂ R

Also, ✂ POQ =✂ SOR (Vertically opposite angles)

Therefore, POQ ~ SOR (AAA similarity criterion)

Example 5 : Observe Fig. 6.30 and then find ✂ P.

Fig. 6.30

Solution : In ABC and PQR,