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Statement:If a line is drawn parallel to one side of a triangle to intersect the
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other two sides in district points, the other two sides are divided in the same
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o t t h e r t t w o s i i d e s i i n d i i s t t r r i i c t t p o i i n t t s , , t t h e o t t h e r t t w o s i i d e s a r e d i i v i i d e d i i n t t h e s a m e
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Given: A triangle ABC in which a line parallel to BC intersects AB at D and AC at E..
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To Prove:
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Construction: Join BE and CD, and draw , and
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Proof:
(1)
Also,
(2)
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Since, and CDE have a common base DE, and are between the parallels s
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DE and BC, hence,

(3)

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From (1), (2) and (3), we get,,
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Theorem:6.2

S t t a t t e m e n t t : : I I f f a l l i i n e d i i v i i d e s a n y t t w o s i i d e s o f f a t t r r i i a n g l l e i i n t t h e s a m e
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Statement : If a line divides any two sides of a triangle in the same
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ratio, the line must bee parallel to the third side.
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