If a line is drawn parallel to one side of a triangle, prove that the other two sides are divided in the same ratio. In the following fig, AB//CD, using the above result solve the following. Find the value of x
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Answer:
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
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