Download Geometry

1.5 Segment and Angle Bisectors
Geometry
What does it mean to bisect
something?
To cut or divide into two equal parts.
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
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
Midpoint Formula
Find the Midpoint
• Plot the points A(-2, 3) and B(5, -2)
• Use the Midpoint Formula to find the
coordinates of the midpoint of segment AB.
• Graph a Segment Bisector
Find the Midpoint
• Plot the points D(3, 5) and E(-4, 0)
• Use the Midpoint Formula to find the
coordinates of the midpoint of segment DE.
• Graph a segment bisector
Find the Other Endpoint of a Segment
• Plot the points X(-3, 1) and M(3, -4)
• The midpoint of segment XY is M. One
endpoint is X. Find the coordinates of the
other endpoint, Y.
• Plot Y
Find the Other Endpoint of a Segment
• Graph the points R(-1, 7) and M(2, 4)
• The midpoint of segment RP is M. One
endpoint is R. Find the coordinates of the
other endpoint, P.
• Plot P
Bisecting an Angle
• An angle bisector is a ray that divides an angle
into two adjacent angles that are congruent.
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?
Example 2
Angle CBA is bisected by ray BD. The measure
of angle DBA is 65 degrees. Find the measure
of angle CBA.
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)