Transcript File - Mrs. Andrews` CBA classes

Lesson 3.3
Segment Bisectors
pp. 94-97
Objectives:
1. To find the midpoint of a segment.
2. To identify bisectors of segments.
3. To identify congruent segments.
Definition
The midpoint of AB is M if A-M-B
and AM = MB.
Theorem 3.1
Midpoint Theorem. If M is the
midpoint of AB, then AM = ½AB.
STATEMENTS
1. M is midpoint of AB
2. AM=MB and A-M-B
3. AM + MB = AB
4. AM + AM = AB
5. 2AM = AB
6. AM = ½AB
REASONS
1. Given
2. Def. of midpoint
3. Def. of betweeness
4. Substitution
5. Distributive prop.
6. Multiplication prop.
Definition
A bisector of a segment is a
curve that intersects the segment
only at the midpoint.
Definition
Congruent segments are
segments that have the same
length. The symbol  is used for
congruent segments.
EXAMPLE Is CD  EF?
C
-7
-5 -3
-1
D
E
1
3
CD = |1 – (-5)| = 6
EF = |9 – 3| = 6
Since CD = EF, CD  EF
F
5
7
9
Practice:
A
-5
Find AB.
AB = 5
C
0
B
D
5
Practice:
A
C
B
D
-5
0
CD  _______
1. AB
2. AC
3. AD
4. None of the above
5
Practice:
A
C
B
D
-5
0
5
What is the coordinate of the midpoint
of AD?
1
Practice: True/False (with reason)
If PQ = QW, then Q is the midpoint of
PW.
False, may not be collinear
Practice: True/False (with reason)
If S the midpoint of GP, then G-S-P.
True, the midpoint of a segment is
between the endpoints
Practice: True/False (with reason)
If BX + XC = BC, then X is the
midpoint of BC.
False, X can be anywhere
between B and C
Homework
pp. 96-97
►A. Exercises
A
B
C
-15 -12 -9
-6
D E
-3
0
F G
3
6
H
I
9 12 15
Use the number line for exercises 110. Find the indicated lengths.
1. FC
►A. Exercises
A
B
C
-15 -12 -9
-6
D E
-3
0
F G
3
6
H
I
9 12 15
Use the number line for exercises 110.
7. Find the coordinate of the
midpoint of FH.
►A. Exercises
Tell whether the following statements
are true or false.
11. If AB  CD, then AB = CD
►A. Exercises
Tell whether the following statements
are true or false.
13. If T is the midpoint of SR, then
S, T, and R are collinear points.
►A. Exercises
Tell whether the following statements
are true or false.
15. If AX + XR = AR, then X is the
midpoint of AR.
►B. Exercises
Given a segment, find the coordinates of
the two endpoints A and B. Assume XB
has the given length and a segment
bisector passes through the point X,
which has the given coordinate. It may
help you to draw a picture.
17. -6, XB = 3
►B. Exercises
Find AB if X is the midpoint of AB and AX
has the given length.
19. 157
►B. Exercises
Use the proper notation to say the
following:
21. Segment XD is congruent to
segment FB.
XD  FB
■ Cumulative Review
26. State the Ruler Postulate.
■ Cumulative Review
27. Where is the most convenient
placement of a ruler to measure AB?
■ Cumulative Review
28. Draw a hexagon
■ Cumulative Review
29. Draw a hexahedron.
■ Cumulative Review
30. Draw a simple curve that bisects a
segment.