1. Segment and Angle Bisectors

2. 1.5 Segment and Angle Bisectors GOAL 1 Bisect a segmentGOAL 2 Bisect an Angle.

3. GOAL 1 BISECTING A SEGMENT 1.5 Segment and Angle Bisectors Vocabulary The point that divides, or bisects, a segment into two congruent segments is called the ________ of the segment. midpoint ZXY In the diagram, Y is the midpoint of if Y is on and This is shown by the red congruence marks.

4. A segment, ray, line, or plane that intersects a segment at its midpoint is called a _______________. segment bisector ZXY T U Name all eight different bisectors of shown above. All eight figures named above are bisectors of

5. x1x1 x2x2 y1y1 y2y2 y x A(x 1, y 1 ) B(x 2, y 2 ) THE MIDPOINT FORMULA If A(x 1, y 1 ) and B(x 2, y 2 ) are points in a coordinate plane, then the midpoint of has coordinates

6. Example: Find the midpoint Find the midpoint of with endpoints D(3, 5) and E(-4, 0). = (–.5, 2.5) Solution (x 1, y 1 )(x 2, y 2 ) = =

7. Example: Find the endpoint The midpoint of is M(3, -4). One endpoint is Y(-3, -1). Find the coordinates of the other endpoint. If the coordinates of X are (x, y), then by the Midpoint Formula Solve: So the other endpoint is X(9, -7). and

8. Checkpoint 1.Find the midpoint of with endpoints P(0, -7) and Q(-2, -1). 2. The midpoint of is One endpoint is J(2, -2). Find the coordinates of the other endpoint.

9. GOAL 2 BISECTING AN ANGLE 1.5 Angles and Their Measures Vocabulary A ray that divides an angle into two adjacent angles that are congruent is called an ____________. angle bisector F H G K In the diagram, bisects since Note the red congruence marks.

10. Example bisects Given that what are the measures of Hint: Draw a sketch! Click to see a sample sketch. H J L K 42° Click for the answer.

11. Example A cellular phone tower bisects the angle formed by the two wires that support it. Find the measure of the angle formed by the two wires. Solution: wire tower ?

12. Example In the diagram bisects The measures of the two congruent angles are Solve for x. M L O N Solution:

13. Checkpoint In the diagram bisects Find x and use it to find A D C B Solution: