Prove that if a line is drawn parallel to one side of a triangle to intersect the other two sides in distinct points, then the other two sides are divided in the same ratio.
Let, us consider ∆ABC in which BC || DE
Given – In ∆ABC, BC || DE
To prove - AD : BD = AE : CE
Proof –
For ∆ABC & ∆ADE,
∠A is common.
As BC || DE
∴ ∠ABC = ∠ADE ………corresponding angles
∴ ∆ABC 
∆ADE ………by AA test of similarity
………corresponding sides of similar triangles
……….by dividend
………by invertendo
∴ AD : BD = AE : EC
Hence, if a line is drawn parallel to one side of a triangle to intersect the other two sides in distinct points, then the other two sides are divided in the same ratio.
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