Question

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

Answer 1

Answer:

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10th

Maths

Triangles

Basic Proportionality Theorem (Thales Theorem)

If a line is drawn parallel...

MATHS

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Asked on October 15, 2019 by

Savneet Saddam

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.

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

solution

Answer 2

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