# 5.2 Perpendicular and Angle Bisectors - PowerPoint PPT Presentation

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5.2 Perpendicular and Angle Bisectors. A point is equidistant from two objects if it is the same distance from the objects. Perpendicular Bisector Theorem. If a point is on the perpendicular bisector of a segment, then it is equidistant from the endpoints of the segment.

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5.2 Perpendicular and Angle Bisectors

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### 5.2 Perpendicular and Angle Bisectors

• A point is equidistant from two objects if it is the same distance from the objects.

### Perpendicular Bisector Theorem

• If a point is on the perpendicular bisector of a segment, then it is equidistant from the endpoints of the segment.

### Converse of the Perpendicular Bisector Theorem

• If a point is equidistant from the endpoints of a segment, then it is on the perpendicular bisector of the segment.

### Using the Perpendicular Bisector Theorem

• What is the length of segment AB?

BA = BC

4x = 6x – 10

-2x = -10

x = 5

AB = 4x

AB = 4 (5)

AB = 20

### Distance from a Point to a Line

• The distance from a point to a line is the length of the perpendicular segment from the point to the line.

• Is also the length of the shortest segment from the point to the line.

### Angle Bisector Theorem

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

### Converse of the Angle Bisector Theorem

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

### Using the Angle Bisector Theorem

• What is the length of segment RM?

RM = RP

7x = 2x + 25

5x = 25

x = 5

RM = 7x

RM = 7 (5)

RM = 35

### More Practice!!!!!

• Homework – Textbook p. 296 – 297 #6 – 22.