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Azz from bhansali public school, asked a question
Subject: Math , asked on 21/8/09

state BPT theorem?

Sonia Verma From Hamdard Public School, added an answer, on 4/9/09
4 helpful votes in Math

 the father of bpt izz thales so it izz know as thales theorem also :if a line izz drawn parallel 2 one side of a triangle 2 interscet the other 2 sides in distinct point then the other 2 sides r divided in the same ratio.if u wanna no converse of bpt reply me.

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Kaushiki From Chickar International School, added an answer, on 6/8/12
73 helpful votes in Math

STATEMENT = If a line is drawn parallel to one side of a triangle divides the other two sides proportionly.

OR

BPT


http://i25.tinypic.com/2r2olz6.jpg

GIVEN = IN TRIANGLE ABC

DE||BC

TO PROVE = AD = AE

BD CE

CONSTRUCTION = DRAW DM AND EN PERPENDICULAR TO AC AND AD RESPECTIVELY. JOIN BE AND CE

PROOF = ar.(TRIANGLE ADE) = 1 x AE x DM

2


ar.(TRIANGLE DEC) = 1 x CE X DM

2


ar.(TRIANGLE ADE) = 1 x AE x DM

ar.(TRIANGLE DEC) 2

1 x CE x DM

2

ar.(TRIANGLE ADE) = AE -------------( i )

ar.(TRIANGLE DEC) CE


ar.(TRIANGLE ADE) = 1 x AD x EN

ar.(TRIANGLE BDE) 2

1 x BD x EN

2


ar.(TRIANGLE ADE) = AD

ar.(TRINAGLE BDE) BD


TRIANGLE BDE AND DEC ARE HAVING SAME BASE AND ARE LYING BETWEEN SAME PARALLEL 'S

SO,

ar.(TRIANGLE BDE) = ar.(TRIANGLE DEC)

ar.(TRIANGLE ADE) = AD -----------( ii )

ar.(TRIANGLE DEC) BD

FROM ( i ) AND ( ii )

AD = AE

BD CE

HENCE, PROVED

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Hayat Gandhi From O P Jindal Modern School, added an answer, on 22/8/09

It is also known as Thales Theorem. It states that 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

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Hayat Gandhi From O P Jindal Modern School, added an answer, on 22/8/09

It is also known as Thales Theorem. It states that 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.

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