Question

Prove that in a triangle, a line dividing two sides proportionally is parallel to the third side.

Answer 1

Given,

⇒

⇒

⇒

⇒

⇒

In ΔABC and ΔADE:

∠A = ∠A (Common angle)

If one angle of a triangle is equal to one angle of the other triangle and the sides including these angles are proportional, then the two triangles are similar.

⇒ ΔABC ∼ ΔADE

∴ ∠ABC = ∠ADE

By converse of corresponding angles axiom, BC || DE

Thus, in a triangle, a line dividing two sides proportionally is parallel to the third side.