1. 1.3 – Segment addition, midpoint, and bisect

2. If point B is between points A and C, then AB + BC = AC
Segment Addition Postulate
If point B is between points A and C, then AB + BC = AC B C A

3. Midpoint:
Point in the middle of a segment that divides the segment into two congruent segments A M B

4. To divide a shape into two equal parts
Bisect:
To divide a shape into two equal parts A M B

5. Ex 1: Use the given figures, to fill in thea.

6. Ex 1: Use the given figures, to fill in theb. = +

7. Ex 1: Use the given figures, to fill in the
bisects c.

8. Ex 2: Sketch, label, and mark the following figures.P A

9. b. W E M

10. c. m O R

11. Ex 3: Use the Segment Addition Postulate to find the indicated length. 36

12. 4 + 17 21

13. 54 – 25 29

14. 32 – 26 6

15. Ex 4: Use the number line to find the indicated distance.

16. 3 9 4 6 6 11 a. AB = _____ b. DA = _____ c. CD = _____ d. BD = _____
e. EC = _____ f. AE = _____ 4 6 6 11

17. Ex 5: In the diagram, points A, B, C, and D are on the same line
Ex 5: In the diagram, points A, B, C, and D are on the same line. AD = 58, AC = 26, and B is the midpoint of AC. Find the indicated lengths. 26 32 13 13 58

18. 13 13
a. AB = _____ b. BC = _____
c. BD = _____ d. CD = _____ 45 32 26 32 13 13 58

19. a. Find RS if RT = 109 in.
RS = _______
54.5
54.5
54.5
109

20. 7 7 P R Q

21. Ex 7: Solve for x. Then find the indicated length.
XY = 2(5) + 3
2x x – 1 = 27
5x + 2 = 27
XY =
5x = 25
XY = 13
x = 5 5 13
a. x = _____ XY = _____

22. 2 11 x2 + 6x – 1 = 15 TV = 6(2) – 1 x2 + 6x – 16 = 0 TV = 11 x +8 x –2
b. x = _____ TV = _____

23. Ex 8: M is the midpoint of each segment below
Ex 8: M is the midpoint of each segment below. Solve for x then find the indicated length.

24. 4x – 12 = -2x + 21
PM = 4(5.5) – 12
6x – 12 = 21
PM = 22 – 12
6x = 33
PM = 10
x = 5.5
5.5 10
c. x = _____ PM = _____

25. 1 7 4x2 + 3x = 7x MN = 7(1) 4x 4x2 – 4x = 0 MN = 7 x – 1 x = 0 x = 1
d. x = _________ MN = _____

26. HJ = 5(4) – 4 5x – 4 + 8x – 10 = 38 HJ = 20 – 4 13x – 14 = 38 13x = 52
9. Point J is between H and K on Use the given information to draw a diagram and write an equation in terms of x. Solve the equation. Then find HJ and JK.
5x – 4
8x – 10 H J K 38
5x – 4 + 8x – 10 = 38
HJ = 5(4) – 4
HJ = 20 – 4
13x – 14 = 38
13x = 52
HJ = 16
x = 4
JK = 8(4) – 10
JK = 32 – 10
JK = 22

27. x +5 x = –5 x –3 x = 3 2x2 + 3x x – 2 28 2x2 + 3x + x – 2 = 28H J K 28
2x2 + 3x + x – 2 = 28
2x2 + 4x – 2 = 28
HJ = 2(3)2 + 3(3)
HJ =
2x2 + 4x – 30 = 0
HJ = 27
2(x2 + 2x – 15) = 0 x +5
x = –5
JK = 3 – 2 x –3
x = 3
JK = 1

28. Ex 10: Solve the real world problem.
You are traveling on a highway staring at point A. After you have traveled 63 miles (point B), you see a sign that says it is 87 miles to your destination (point C).

29. a. Find the total distance you will travel to get to your destination.=
150 mi

30. 60t = 150
t = 2.5hrs