Chapter 5.1 Segment and Angle Bisectors Remember the Distance Formula!!

Perpendicular Bisector Theorem Theorems Perpendicular Bisector Theorem If a point lies on the ______________ bisector of a segment, then it is _______________ from the endpoints of the segment. perpendicular equidistant

Perpendicular Bisector Theorem =Distance =Distance Line segment endpoint endpoint

Theorems Converse of Perpendicular Bisector Theorem

Converse of Perpendicular Bisector Theorem =Distance =Distance Line segment endpoint endpoint

Angle Bisector Theorem Theorems Angle Bisector Theorem bisector If a point lies on the ____________ of an angle, then it is _____________ from both sides of the angle. equidistant

Theorems Converse of Angle Bisector Theorem

Angle Bisector Theorem =Distance =Distance side of <G side of <G G

Distance Formula MIDPOINT Formula

Slope Formula

Examples Graph the line segment then construct a perpendicular bisector. 1. Get a piece of graph paper. 2. Graph the line segment AB . A ( -2, 5) B ( 4, -3). 3. Find the midpoint and slope of AB . ( slope). 4. Plot the midpoint, and count the slope. 5. Highlight the perpendicular bisector.

Examples Construct an angle bisector 1. Draw an angle (of any size) 2. Use a compass and make an arc (from the vertex) that intersects both sides of the angle 3. Mark the points where the arc intersects the sided. 4. Using the same radius (on the compass), make another arc from both points of intersection. 5. Mark the point where these two arcs intersect 6. Draw a line from the arc intersection through the vertex of the angle