Question

prove BPT theorem (Thales theorem )​

Answer 1

Answer:

I think it help you dear ✌️✌️✌️✌️

Answer 2

Answer:

AD/DB = AE/EC

Explanation:

> If a line 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 :

∆ABC Where DE || BC

TO PROVE:

AD/DB = AE/EC

CONSTRUCTION:

Join BE and CD

Draw DM perpendicular AC

EN Perpendicular AB

PROOF:

ar(ADE) = 1/2 × base × height

= 1/2 × AD × EN ......(1)

ar(BDE) = 1/2 × base × height

= 1/2 × DB × EN ......(2)

ar(ADE) = 1/2 × base × height

= 1/2 × AE × DM ....(3)

ar(DEC) = 1/2 × base × height

= 1/2 × EC × DM .....(4)

> DIVIDE (1) & (2)

ar(ADE) / ar(BDE)

= 1/2 × AD × EN / 1/2 × DB × EN

= AD/DB......(A)

>DIVIDE (3) & (4)

ar(ADE) / ar(DEC)

= 1/2 × AE × DM / 1/2 × EC × DM

= AE / EC......(B)

NOW,

∆BDE and ∆DEC are on the same base DE and between the same parallel lines BC and DE

= ar(BDE) = ar(DEC)

Hence,

ar(ADE) / (BDE) = ar(ADE) / ar( DEC)

= AD/DB = AE/EC

( from A & B )

HENCE PROVED...