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Parallel Lines & Proportional Parts

Parallel Lines & Proportional Parts

Author: Kyle Webb
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Tutorial

Triangle Proportionality Theorem & Converse

Theorem 6.4 Triangle Proportionality Theorem
If a line is parallel to one side of a triangle and intersects the other sides, it divides the two sides proportionally.

Theorem 6.5 Converse of the Triangle Proportionality Theorem
If a line divides two sides of a triangle proportionally, then it is parallel to the third side.

Source: McDougal Littel High School Geometry

Triangle Midsegment Theorem

"How to prove and use properties of triangle midsegments. Yeah, it's that important."

Corollary: Parallel Lines and Transversals

If three or more parallel lines intersect two transversals, then they cut off the transversals proportionally.

In the figure shown, if stack A D with left right arrow on top parallel to stack B E with left right arrow on top parallel to stack C F with left right arrow on top, then fraction numerator A B over denominator B C end fraction equals fraction numerator D E over denominator E F end fraction comma fraction numerator A C over denominator E F end fraction equals fraction numerator B C over denominator E F end fraction and fraction numerator A C over denominator B C end fraction equals fraction numerator D F over denominator E F end fraction

Example found at the bottom of this page: http://hotmath.com/hotmath_help/topics/parallel-lines-and-transversals.html