5.1 Perpendicular and Angle Bisectors Guiding Question:

Vocabulary/Theorems Equidistant: when a point is the same distance from two or more objects 5-1-1: Perpendicular Bisector Theorem: If a point is on the perpendicular bisector of a segment, then it is equidistant from the endpoints of the segment. XA=XB X A B Y

5-1-2 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 a segment. XY AB YA ~ YB X A B Y

5-1-3 Angle Bisector Theorem: if a point is on the bisector of an angle, then it is equidistant from the sides of the angle 5-1-4 Converse of the Angle Bisector Theorem: If a point in the interior of an angle is equidistant from the sides of the angle, then it is on the bisector of the angle. A AC=BC C B P ˂APC ˂BPC

Perpendicular Bisector Find the measure of MN Example 1: Example 2: 2.6 M L P Find the measure of BC B 38 A D 12 38 C

Angle Bisector Example 3 Example 4 Find the measure of BC 7.2 D A G Find the m<EFH, given that m<EFG=50 H E F

Homework DUE WEDNESDAY! Page 304: 2-8 even, 12-16 even