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Proportionality
in Triangles
Proportional Segments
Two line segments are divided
proportionally when the ratio of the
lengths of the segments of one of
them is equal to the ratio of the
lengths of the segments of the other.
Side-Splitting Theorem
If a line is parallel to one side of a
triangle and intersects the other sides
at any points except at its vertex, then
a triangle similar to the given triangle
is formed and the line divides the sides
proportionally.
Converse of Side-Splitting Theorem
If a line intersects two sides of triangle
and divides them proportionally, then
the line is parallel to the third side.
Proportional Segments Theorem
If three parallel lines intersect two
transversals, then the segments
intercepted on the transversals are
proportional.

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6 lesson 4 proportionality in triangles

  • 2. Proportional Segments Two line segments are divided proportionally when the ratio of the lengths of the segments of one of them is equal to the ratio of the lengths of the segments of the other.
  • 3. Side-Splitting Theorem If a line is parallel to one side of a triangle and intersects the other sides at any points except at its vertex, then a triangle similar to the given triangle is formed and the line divides the sides proportionally.
  • 4. Converse of Side-Splitting Theorem If a line intersects two sides of triangle and divides them proportionally, then the line is parallel to the third side.
  • 5. Proportional Segments Theorem If three parallel lines intersect two transversals, then the segments intercepted on the transversals are proportional.