1. Lesson 3.3
Segment Bisectors pp

2. Objectives:
1. To find the midpoint of a segment.
2. To identify bisectors of segments.
3. To identify congruent segments.

3. Definition
The midpoint of AB is M if A-M-B and AM = MB.

4. Theorem 3.1
Midpoint Theorem. If M is the midpoint of AB, then AM = ½AB.

5. STATEMENTS REASONS
1. Given
1. M is midpoint of AB
2. AM=MB and A-M-B
2. Def. of midpoint
3. AM + MB = AB
3. Def. of betweeness
4. Substitution
4. AM + AM = AB
5. 2AM = AB
5. Distributive prop.
6. AM = ½AB
6. Multiplication prop.

6. Definition
A bisector of a segment is a curve that intersects the segment only at the midpoint.

7. Definition
Congruent segments are segments that have the same length. The symbol  is used for congruent segments.

8. EXAMPLE Is CD  EF? CD = |1 – (-5)| = 6 EF = |9 – 3| = 6-7 -3 -1 5 7
CD = |1 – (-5)| = 6
EF = |9 – 3| = 6
Since CD = EF, CD  EF

9. Practice: 5 -5 A B C D
Find AB.
AB = 5

10. Practice: 5 -5 A B C D
CD  _______
1. AB
2. AC
3. AD
4. None of the above

11. Practice: 5 -5 A B C D
What is the coordinate of the midpoint of AD? 1

12. False, may not be collinear
Practice: True/False (with reason)
If PQ = QW, then Q is the midpoint of PW.
False, may not be collinear

13. True, the midpoint of a segment is between the endpoints
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

14. 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

15. Homework pp

16. Use the number line for exercises 1-10. Find the indicated lengths.
►A. Exercises
Use the number line for exercises Find the indicated lengths.
1. FC
A B C D E F G H I

17. Use the number line for exercises 1-10. 7. Find the coordinate of the
►A. Exercises
Use the number line for exercises 1-10.
7. Find the coordinate of the
midpoint of FH.
A B C D E F G H I

18. ►A. Exercises
Tell whether the following statements are true or false.
11. If AB  CD, then AB = CD

19. ►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.

20. ►A. Exercises
Tell whether the following statements are true or false.
15. If AX + XR = AR, then X is the midpoint of AR.

21. ►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

22. ►B. Exercises
Find AB if X is the midpoint of AB and AX has the given length.

23. 21. Segment XD is congruent to segment FB.
►B. Exercises
Use the proper notation to say the following:
21. Segment XD is congruent to segment FB.
XD  FB

24. ■ Cumulative Review
26. State the Ruler Postulate.

25. ■ Cumulative Review
27. Where is the most convenient placement of a ruler to measure AB?

26. ■ Cumulative Review
28. Draw a hexagon

27. ■ Cumulative Review
29. Draw a hexahedron.

28. ■ Cumulative Review
30. Draw a simple curve that bisects a segment.