1.3 – Segment addition, midpoint, and bisect

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

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

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

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

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

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

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

b. W E M

c. m O R

Ex 3: Use the Segment Addition Postulate to find the indicated length. 24 + 12 36

4 + 17 21

54 – 25 29

32 – 26 6

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

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

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

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

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

7 7 P R Q

Ex 7: Solve for x. Then find the indicated length. XY = 2(5) + 3 2x + 3 + 3x – 1 = 27 5x + 2 = 27 XY = 10 + 3 5x = 25 XY = 13 x = 5 5 13 a. x = _____ XY = _____

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

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.

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 = _____

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

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

x +5 x = –5 x –3 x = 3 2x2 + 3x x – 2 28 2x2 + 3x + x – 2 = 28 H J K 28 2x2 + 3x + x – 2 = 28 2x2 + 4x – 2 = 28 HJ = 2(3)2 + 3(3) HJ = 18 + 9 2x2 + 4x – 30 = 0 HJ = 27 2(x2 + 2x – 15) = 0 x +5 x = –5 JK = 3 – 2 x –3 x = 3 JK = 1

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).

a. Find the total distance you will travel to get to your destination. 63 + 87 = 150 mi

60t = 150 t = 2.5hrs