1.5 Segment

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1.5 Segment Angle Bisectors
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Always Remember!

• If they are congruent, then set their measures
  equal to each other!

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Goal 1 Bisecting a Segment

• Midpoint The point that bisects a segment.
• Bisects?
• splits into 2 equal pieces

A M B
12x3 10x5
12x310x5 2x2 x1
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Segment Bisector

• A segment, ray, line, or plane that intersects a
  segment at its midpoint.

k
A
M
B
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Compass Straightedge

• Tools used for creating geometric constructions
• We will do an activity with these later.

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Midpoint Formula

• Used for finding the coordinates of the midpoint
  of a segment in a coordinate plane.
• If the endpoints are (x1,y1) (x2,y2), then

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Example Find the midpoint of SP if S(-3,-5)
P(5,11).
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Example The midpoint of AB is M(2,4). One
endpoint is A(-1,7). Find the coordinates of B.
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Goal 2 Bisecting an Angle

• Angle Bisector A ray that divides an angle into
  2 congruent adjacent angles.
• BD is an angle bisector of ltABC.

A
D
B
C
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Example If FH bisects ?EFG m?EFG120o, what
is m?EFH?
E
H
F
G
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Last Example Solve for x.
If they are congruent, set them equal to each
other, then solve!

x40o
x40 3x-20 40 2x-20 60 2x 30 x
3x-20o
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Activity Time

• Use your compass, protractor and straightedge to
  work on the three activities in this section.
• Pg 33, 34, 36