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Geometry

Geometry. 1.5 Segment and Angle Bisectors. 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.

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Geometry

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  1. 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 atits 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 bisectoris a ray that divides an angle into two adjacent angles that are congruent.

  8. Example 1 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?

  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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