Proportions in triangles
MathDefinition
When a line is drawn parallel to one side of a triangle, it divides the other two sides proportionally. This principle extends to angle bisectors, which divide the opposite side in the ratio of the adjacent sides.
Examples
- A midsegment is parallel to the third side and half its length
- If DE ∥ BC in triangle ABC, then AD/DB = AE/EC
- An angle bisector in a triangle with sides 6 and 9 divides the opposite side in ratio 6:9 = 2:3
Study This Concept
Practice proportions in triangles with free review games in these units: