Maths

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.
Solution : In ABC and PQR,
Fig. 6.30