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 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.

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? 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

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

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

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

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

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

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

Use the number line for exercises 1-10. Find the indicated lengths. ►A. Exercises Use the number line for exercises 1-10. Find the indicated lengths. 1. FC -15 -12 -9 -6 -3 0 3 6 9 12 15 A B C D E F G H I

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. -15 -12 -9 -6 -3 0 3 6 9 12 15 A B C D E F G H I

►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

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

■ 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.