Question

prove that : if a line parallel to a side of a triangle intersect the remaining sides in two distinct points the line divides the sides in the same proportion. ( please solve it step by step with figure)​

Answer 1

Given: PR || BC , AB and AC are transversal

Proof:

∠APR = ∠ABC ..corresponding

∠ARP = ∠ACB ..Corresponding

•°• By AA test of similarity two triangle are similar.

△ABC = △APR

• Corresponding sides of similar triangle:

• •°• AB/AP = AC/AR

(AP + BP)/AP = (AR + CR)/AR

•°• BP/AP = CR/AR

Hence proved,,

Refer attachment for diagram