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