Perpendiculars and Bisectors II

Distance from a Point to a Line

• Length of the perpendicular segment from the point to the line.

• A point is equidistant from two lines if it is the same distance from each line.

• If a point is on the bisector of an angle, then it is equidistant from the two sides of the angle.

Theorem: Angle Bisector

If m∠BAD = m∠CAD, then DB = DC.

• If a point is on the interior of an angle and is equidistant from the two sides of the angle, then it lies on the bisector of the angle.

Theorem: Angle Bisector Converse

If DB = DC, then m∠BAD = m∠CAD.

m∠BAD = m∠CAD

Using Angle Bisectors

Checkpoint

Using Angle Bisectors

Homework

• Exercise 5.1 page 267: 1-37, all.