Question

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

Answer 1

Step-by-step explanation:

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.

[ Basic Proportionality Theorem

Or Thales Theorem ]

Given:

In ∆ABC , which intersects AB and AC at D and F respectively.

RTP:

Construction:

Join B , E and C ,D and then draw

.

Proof:

Area of ∆ADE =

Area of ∆BDE =

So,ar(∆ADE)/ar(∆BDE)

=

=----(1)

Again Area of ∆ADE =

Area of ∆CDE =

So,ar(∆ADE)/ar(∆CDE)

=

= ------(2)

Observe that ∆BDE and ∆CDE are on the same base DE and between same parallels BC and DE.

So ar(∆BDE) = ar(∆CDE) ---(3)

From (1),(2) & (3),. we have

=

Hence , proved .

Answer 2

Answer:

You can also check the Maths NCERT of class 10. It's the Theorem 6.1(pg124)

Step-by-step explanation:

In the figure we have triangle ABC and DE is parallel to BC

We have to prove that AD/DB = AE/EC

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