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5.1 Perpendicular and Angle Bisectors

5.1 Perpendicular and Angle Bisectors. Guiding Question:. Vocabulary/Theorems. Equidistant: when a point is the same distance from two or more objects

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5.1 Perpendicular and Angle Bisectors

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  1. 5.1 Perpendicular and Angle Bisectors Guiding Question:

  2. 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

  3. 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

  4. 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

  5. Perpendicular Bisector N 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

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

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

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