Question

prove that if draw a line which is parallal to any side of a triangle and intersect the other two sides at different points , then then this line divides these two line in the same ration.
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Answer 1

Answer:

Prove that if a line is drawn parallel to one side of a triangle to intersect the other two sides

Theorem: 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.

Step-by-step explanation:

Answer 2

Answer:

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

Hence proved