Q) State and prove Basic Proportionality Theorem.

OR

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 other two sides are divided in the same ratio.

(Q32 A – 30/1/3 – CBSE 2026 Question Paper)

Ans: 

VIDEO SOLUTION

STEP BY STEP SOLUTION

Step 1: Let’s make a Δ ABC.

Next, we mark D and E as two distinct points on AB and AC respectively, such that DE ǁ BC.

Next, we mark two points M and N be on AD and AE.

Join ME such that ME ⊥ AD and similarly, join DN, such that DN ⊥ AE.

Next, we connect DC and BE.

We need to prove that 

Step 2: In Δ ADE and Δ BDE,

=

=              —- (1)

Similarly, in Δ AED and Δ CED,

=

=              —- (2)

Step 3: Next, in Δ BDE and Δ CED:

∵  Area of triangles between two same parallel sides with same base are equal

∴ Area Δ BDE = area Δ CED           —-(3)

Step 4: Next, from equation 1 and equation 3; we get:

     (from equation 3)

By putting values from equation 1 and equation 2, we get:

Hence Proved !

[Note: This is proving of Basic Proportionality Theorem (BPT). Learn to write all steps! ]

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