In figure 6.27,

Prove that BR = CS.

In Δ ABC

Given, A-P- B, B- R-S-C and A-Q-C

and

To prove – BR = CS

Proof : In Δ ABC given

∴ ………..eq(1)

(∵ If a line to one side of a Δ intersects the other two sides of the Δ in distinct points, the segments of the other sides of the Δ in the same half plane of the line are proportional to the corresponding sides of the Δ)

Similarly,

∴ ………………..2

From 1 and 2, we get

……..eq(3)

Similarly,

∴ ……………4

From 3 and 4

⇒ BR = CS hence proved