7
Question
Prove that in a triangle, a line dividing two sides proportionally is parallel to the third side.
Prove that in a triangle, a line dividing two sides proportionally is parallel to the third side.
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Solution
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.
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.
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