This document discusses properties of perpendiculars, bisectors, and equidistance as they relate to points, lines, and angles. It states that the distance from a point to a line is the length of the perpendicular segment, and a point is equidistant from two lines if it is the same distance from each. It also presents theorems that if a point is on the bisector of an angle, it is equidistant from the two sides, and if a point within an angle is equidistant from the sides, it lies on the bisector.

1. Perpendiculars and Bisectors II

2. 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.

3. 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.

4. 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

5. Using Angle Bisectors

6. Checkpoint

7. Using Angle Bisectors

8. Homework Exercise 5.1 page 267: 1-37, all.