Question

In the given figure, l || m

(i) Name three pairs of similar triangles with proper correspondence; write similarities.
(ii) Prove that $\frac{\mathrm{AB}}{\mathrm{PQ}}=\frac{\mathrm{AC}}{\mathrm{PR}}=\frac{\mathrm{BC}}{\mathrm{RQ}}$

Answer 1

(i) Three pair of similar triangles are-

$∆ABK~∆PQK$ (AAA Similarity)

$∆CBK~∆RQK$ (AAA Similarity)

$∆ACK~∆PRK$ (AAA Similarity)

(ii) Since the pair of similar triangles mentioned above can give us the desired result. The ratios of the corresponding side of the similar triangle are equal.

So,

Therefore,

……equation (1)

Similarly in ,

……equation (2)

Similarly ,

……equation (3)

From the above equations 1 and 2 we have,

=

……eqaution (4)

Combining it with equation (4)

hence proved