Question

Prove that if a line is drawn parallel to one side of a triangle to intersect
the other two sides, then the two sides are dividedin the same ratio.​

Answer 1

Answer:

10th

Maths

Triangles

Basic Proportionality Theorem (Thales Theorem)

If a line is drawn parallel...

MATHS

If a line is drawn parallel to one side of a triangle to intersect the other two sides in distinct points then prove that the two sides are divided in the same ratio.

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VIDEO EXPLANATION

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