Question

HEY GUYS...


STATE BASIC PROPORTIONALITY THEOREM.... ​

Answer 1

Hey mate

Here's your answer:-

《BASIC PROPORTIONAL THEOREM (BPT) 》

Statement:-

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.

Given:-

A triangle ABC in which a line parallel to side BC intersects other two sides AB and AC at D and E respectively.

To Prove:-

AD/DB = AE/EC.

Construction:-

Let join BE and CD and then draw DM perpendicular to AC and EN perpendicular to AB.

Proof:-

Now, Area of Triangle ADE = 1/2×base×height

1/2×AD×EN

So, ar(ADE) = 1/2×AD×EN

Similarly, ar(BDE) = 1/2×DB×EN

ar(ADE) = 1/2× AE× DM

ar(DEC) = 1/2×EC×DM.

Therefore, ar(ADE)/ar(BDE)

1/2×AD×EN/1/2×DB×EN

then we get AD/DB ----------- (i)

and, ar(ADE)/ar(DEC)

1/2×AE×DM/1/2×EC×DM

then we get AE/EC ------------ (ii)

Triangle BDE and triangle DEC are on the same base DE and between the same parallels BC and DE.

So, ar(BDE) = ar(DEC) -------(iii)

Therefore from equation (i) , (ii) and (iii) we have:-

AB/DB = AE/AC ( HENCE PROVED)

Hope it's helps you mate♡

Answer 2

Answer:

Basic Proportionality Theorem, also called Thales theorem, states that, " If a straight line is drawn parallel to the third side of a triangle, it divides the other two sides proportionally"