1. 5.1 Perpendiculars and Bisectors

2. Perpendicular Bisector Theorem If a point is on the perpendicular bisector of a segment, then it is equidistant from the endpoints of the segment. If CP is the perpendicular bisector of AB, then CA = CB. A P B C

3. 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. If CA=CB, then C lies on the perpendicular bisector of

4. In the diagram shown, MN is the perpendicular bisector of ST. What segment lengths in the diagram are equal? Explain why Q is on MN T M N S Q 12

5. Angle Bisector Theorem If a point is on the bisector of an angle, then it is equidistant from the two sides of the angle. If m<BAD = m<CAD, then DB = DC. A B C D

6. Converse of the Angle Bisector Theorem If a point is in the interior of an angle and is equidistant from the sides of the angle, then it lies on the bisector of the angle. If DB=DC, then m<BAD = m<CAD

7. Use the diagram to answer the following. In the diagram, F is on the bisector of < DAE. If m<BAF = 50, then m<CAF = ____ If FC = 10, then FB = ____ Is triangle ABF congruent to triangle ACF? Explain. A B D G F C E

8. Closing Question: