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1.5 Segment & Angle Bisectors. Goals:. Students will understand geometric concepts and applications. Bisect a segment. Bisect an angle. Remember!. Congruent means,… equal to each other!. Midpoint. The point that bisects a segment. Bisects ? splits into 2 equal pieces. 12x+3=10x+5

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1 5 segment angle bisectors

1.5 Segment & Angle Bisectors


Goals
Goals:

Students will understand geometric concepts and applications.

  • Bisect a segment.

  • Bisect an angle.


Remember
Remember!

  • Congruent means,…

  • equal to each other!


Midpoint
Midpoint

  • The point that bisects a segment.

  • Bisects?

    splits into 2 equal pieces

12x+3=10x+5

2x=2

x=1

A M B

12x+3 10x+5


Segment bisector
Segment Bisector

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

k

A

M

B


Midpoint formula
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


Ex find the midpoint of sp if s 3 5 p 5 11
Ex: Find the midpoint of SP if S(-3,-5) & P(5,11).


Ex the midpoint of ab is m 2 4 one endpoint is a 1 7 find the coordinates of b
Ex: The midpoint of AB is M(2,4). One endpoint is A(-1,7). Find the coordinates of B.


Angle bisector
Angle Bisector

  • A ray that divides an angle into 2 congruent adjacent angles.

    BD is an angle bisector of <ABC.

A

D

B

C


Ex if fh bisects efg m efg 120 o what is m efh
Ex: If FH bisects EFG & mEFG=120o, what is mEFH?

E

H

F

G


Last example solve for x
Last example: Solve for x.

* If they are congruent, set them equal to each other, then solve!

x+40o

x+40 = 3x-20

40 = 2x-20

60 = 2x

30 = x

3x-20o


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