Question

STATE THE BASIC PROPORTIONALITY THEOREM

No spam ​

Answer 1

Answer:

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

______

Answer 2

Hey mate here is your answer

Basic Proportionality Theorem:

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

Solution:

Given : In ∆ ABC in which a line parallel to side BC intersect other two sides AB and AC at D and E respectively

To prove: AD =AE

DB EC

Construction: Join BE and CD and draw DM Perpendicular to AC

To proof : Area of ∆ADE =1/2×AD×EN

So, ar (ADE)=1/2×AD×EN _______(1)

ar(BDE) =1/2×DB×EN________(2)

Dividing the equation (1) & (2)

ar(ADE) = 1/2×AD×EN

ar(BDE)=1/2×DB×EN

ar (ADE)=AD ________(5)

ar(BDE)=DB

Similarly ar(ADE)=1/2×AE×DM ________(3)

ar(DEC)=1/2×EC×DM_________(4)

Dividing the equation (3) & (4)

ar(ADE)=1/2×AE×DM

ar(DEC)=1/2×EC×DM

ar(ADE)= AE _______(6)

ar(DEC)=EC

∆BDE and ∆DEC are on the same baseand lie between the same parallels BC & DE

So, ar∆BDE=ar∆DEC

From equation (5)& (6)

AD = AE

DB EC

Hence Proved

Hope it will help you ✌️