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Segment and Angle Bisectors
Unit 1 Day 5

Do Now
 Find the average of -2 and 5.
Bisecting a Segment
 Bisect: to divide a figure into two congruent parts
 The ___________ of a segment is the point that
bisects it.
 A segment bisector is a segment, ray, line, or plane
that intersects a segment at __________________.
Midpoint Formula
 The midpoint of two coordinates is found by
taking their ______________.
 For (x1, y1) and (x2, y2), the midpoint has
coordinates
Midpoint Formula
 Ex. 1 Find the coordinates of the midpoint of (-2, 3) and
(5, -2).
 Ex. 2 The midpoint of segment AB is (2, 4). If A is (-1, 7),
find the coordinates of B.
Angle bisector
 An angle bisector is a _____________ that divides an
angle into two adjacent angles that are congruent.
Angle Bisectors
 Ex. 3 Ray FH bisects angle EFG. Given that mEFG =
120, what is mEFH?
Angle Bisectors
 Ex. 4 Angle JKL is bisected by ray KM. Given that
the two congruent angles are as labeled, what is
mJKM?
Constructing Midpoints
 Materials: compass, straightedge, paper, pencil
 Use the straightedge to draw a segment. Call it AB.
 Place the compass at point A. Open the compass more than
half the length of AB, and draw an arc.
 Keep the same opening and repeat with the compass at point
B. The two arcs should intersect.
 Use a straightedge to draw a segment connecting the two
points where the arcs intersect each other.
Constructing Angle Bisectors
 Use the straightedge to draw an angle. Label it C.
 Place the compass at point C. Draw an arc that intersects both
sides of the angle. Label the points of intersection A and B.
 Place the compass at point A. Draw a small arc.
 Keep the same compass opening and repeat at point B. The
two small arc should intersect.
 Label that intersection point D. Use a straightedge to draw ray
CD.