Prove that if a line is drwan prallel to one side of a triangle to intersect the other two side in distinct points, the other two side are divided in the same ratio?
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Given:
DE∣∣BC
To prove that:
AE
EC
=
AD
BD
Proof:
∠AED=∠ACB Corresponding angles
∠ADE=∠ABC Corresponding angles
∠EAD is common to both the triangles
⇒ΔAED∼ΔACB by AAA similarity
⇒
AE
AC
=
AD
AB
⇒
AE
AE+EC
=
AD
AD+BD
AE
EC
=
AD
BD
Hence proved
sujanlegend:
where is diagram
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