Proportions in triangles

Math

Definition

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: