If F is on the perpendicular bisector of

If F is on the perpendicular bisector of segment AB and AF = 5 x - 20 , BF = 3 x + 18, what is the value of x and AF ?

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 4 x = 6 x – 10 -2 x = -10 x=5 AB = 4 x 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 7 x = 2 x + 25 5 x = 25 x=5 RM = 7 x RM = 7 (5) RM = 35

More Practice!!!!! • Homework – Textbook p. 296 – 297 #6 – 22.