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1.5 Segment and Angle Bisectors

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1 1.5 Segment and Angle Bisectors
Geometry 1.5 Segment and Angle Bisectors

2 Bisecting a Segment The midpoint of a segment is the point that divides, or bisects, the segment into two congruent segments. A segment bisector is a segment, ray, line, or plane that intersects a segment at its midpoint

3 Finding the Midpoint If you know the coordinates of the endpoints of a segment, you can calculate the coordinates of the midpoint. You simply take the mean, or average, of the x-coordinates and of the y-coordinates. This method is summarized as the Midpoint Formula

4 Midpoint Formula

5 Find the Midpoint Graph the points A(-2, 3) and B(5, -2)
Use the Midpoint Formula to find the coordinates of the midpoint of segment AB.

6 Find the Midpoint Graph the points D(3, 5) and E(-4, 0)
Use the Midpoint Formula to find the coordinates of the midpoint of segment DE.

7 Bisecting an Angle An angle bisector is a ray that divides an angle into two adjacent angles that are congruent.

8 The ray FH bisects the angle EFG
The ray FH bisects the angle EFG. Given that the measure of angle EFG = 120 degrees, what are the measures of angle EFH and angle HFG? Example 1

9 Example 2 Angle CBA is bisected by ray BD. The measure of angle DBA is 65 degrees. Find the measure of angle CBA.

10 Example 3 In the diagram, ray RQ bisects angle PRS. The measures of the two congruent angles are (x+40) degrees and (3x – 20) degrees. Solve for x. (x + 40) (3x – 20)


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