6 lesson 4 proportionality in triangles
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This document discusses proportionality in triangles. It defines proportional line segments as those where the ratio of lengths on one segment equals the ratio on the other. The side-splitting theorem states that if a line parallel to one side of a triangle intersects the other two sides, it divides them proportionally and forms a similar triangle. The converse of this theorem is that if a line divides two sides of a triangle proportionally, then it is parallel to the third side. The proportional segments theorem says that if three parallel lines intersect two crossing lines, the segments formed 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.