Chapter 5 Congruent Triangles

Section 6 Angle Bisectors and Perpendicular Bisectors

The ___________________________________________________________ is measured by the length of the perpendicular segment from the point to the line. When a point is the same distance from one line as it is from another line, the point is __________________________ from the two lines.

Example 1: Use the Angle Bisector Theorem Statements Reasons 1) 1) 2) 2) 3) 3) 4) 4) 5) 5)

Perpendicular Bisectors A segment, ray, or line that is perpendicular to a segment at its midpoint is called a perpendicular bisector.

Example 2: Use Perpendicular Bisectors Use the diagram to find AB.

Checkpoint: Use Angle Bisectors and Perpendicular Bisectors

Example 3: Use the Perpendicular Bisector Theorem In the diagram, MN is the perpendicular bisector of ST. Prove that ∆MST is isosceles. Statements Reasons 1) 1) 2) 2) 3) 3)

Example 4: Use Intersecting Bisectors of a Triangle A company plans to build a warehouse that is equidistant from each of its three stores, A, B, and C. Where should the warehouse be built?

EXIT SLIP