Segment and Angle Bisectors 1 5 Segment and

Segment and Angle Bisectors

1. 5 Segment and Angle Bisectors GOAL 1 Bisect a segment GOAL 2 Bisect an Angle.

1. 5 GOAL Segment and Angle Bisectors 1 BISECTING A SEGMENT Vocabulary The point that divides, or bisects, a segment into two midpoint of the segment. congruent segments is called the ____ X Y Z In the diagram, Y is the midpoint of if Y is on and This is shown by the red congruence marks.

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

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 y y 2 y 1 B(x 2, y 2) A(x 1, y 1) x 1 x 2 x

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

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 and Solve: So the other endpoint is X(9, -7).

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

1. 5 GOAL Angles and Their Measures 2 BISECTING AN ANGLE Vocabulary A ray that divides an angle into two adjacent angles that are angle bisector congruent is called an ______. In the diagram, since F bisects K H Note the red congruence marks. G

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

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. ? wire tower Solution:

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

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