prove that a line is drawn parallel to one side of a triangle to intersect the other two sides in distinct points the other two sides are divided in the same ratio
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step by step method.
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Answer:
Step-by-step explanation:
Given:
DE∣∣BC
To prove that
EC/AE=BD/AD
proof:
∠AED=∠ACB Corresponding angles
∠ADE=∠ABC Corresponding angles
∠EAD is common to both the triangles
⇒ΔAED∼ΔACB by AAA similarity
⇒ AC/AE=AB/AD
(AE+EC)/AE=(AD+BD)/AD
EC/AE=BD/AD
⇒
AE
AE+EC
=
AD
AD+BD
⇒
AE
EC
=
AD
BD
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