Assignment 6.5 is an introduction to proportion theorems resulting from a line segment with one endpoint at the vertex of a triangle and the other endpoint on the opposite side.

Prerequisite Skills: Calculate cross-products (Assignment 6.2). Solve proportions (Assignment 6.2). Solve algebraic equations with one variable. Evaluate algebraic expressions.

Theorems: The bisector of an angle of a triangle divides the side opposite the angle into two segments. The lengths of the segments are proportional to the

lengths of the other two sides of the triangle.

If a ray from the vertex of a triangle divides the opposite side into lengths that are proportional to the lengths of the other two sides of the triangle, then

the ray bisects the angle.

Geometry for School and Home

Assignment 6.5

Proportions in Triangles: Angle Bisectors

Objectives

Develop and apply a theorem about proportional line segment lengths in triangles with an angle bisector.

Use the converse of the theorem to identify angle bisectors.

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​Assignment 6.5

​Proportions in Triangles: Angle Bisectors