1. It All Adds Up SEGMENT ADDITION POSTULATE

2. Do Now Complete the following problems by using a number line: Draw point A at 6 Draw a segment from 3 to 8, what is the distance? What is the distance between points -2 and 6? 7 and 1? Can the distance of a line ever be negative? Why/why not? Can we measure the distance of a ray? A line?

3. Objective Solve for the length of segments by applying the Segment Addition Postulate Why it matters in THIS CLASS: Many aspects of Geometry are applications of algebra. By applying the Segment Addition Postulate we will also be strengthening our algebraic skills. Why it matters in LIFE: Segment Addition Postulate helps us to calculate the distance between various points. Understanding the concepts behind this theory can aid us in planning any trips or movement in our own lives.

4. Run Geometry! Your track coach tells you that you have two options in practice. You can either run 1.5 miles and then 4.5 miles, or run 3 miles and then 2.5 miles through. Which would you choose and why? Be prepared to vote!

5. Segment Addition Postulate If we have two segments, EG and GF, how can we find the length of EF, once we know that EG is 2 and GF is 7. F is between G and H. If we know GF is 7 and GH is 8, what is FH? What mathematical operation did we have to use here? What can you conclude from these examples?

6. Segment Addition Postulate If 3 points A, B, & C are collinear & B is between A & C, then AB + BC = AC A B C Part + Part = Whole

7. Practice Draw a picture to help visualize which segment you are solving for. B lies between A and C. Given AB = 4 and AC = 5, what is BC?

8. Practice Draw a picture to help visualize which segment you are solving for. A and D are the endpoints of a segment, B and C lie in the middle. Given AB = 2, BC = 9, and CD = 3, what is AD? What is BD?

9. Check Your Understanding If we knew AB and BC, what operation would we do to find AC? If we knew AB and AC, how could we find BC? If we knew BC and AC, how can we find AB? What generalizations can you apply here? Part + Part = Whole Whole – Part = Part

10. Segment Addition Postulate With Variables First, what does a variable do in math? AB = 5, BC = y + 1, AC = 8. Solve for y

11. Practice Draw a picture to help visualize which segment you are solving for. GE = y + 5, EH = y – 2, GH = 11. Solve for y and the missing lengths

12. Practice Draw a picture to help visualize which segment you are solving for. Given T is between R and S RT = 2x, ST =16, RS= 5x + 7. Solve for x and each length

13. Check Your Understanding How could you check your work once you have applied the Segment Addition Postulate with variables?

14. Independent Practice 1.Given GE = 11 and GH = 15, what is EH? 2.M is between L and N. Find MN if LN = 20 and LM = 15 3. S is between D and T. Find DS if DT = 60, DS = 2x – 8, and ST = 3x – 12 4. Point B is between points A and C on a line. AC = 75, AB = x + 15, and BC = 5x Draw a picture and find AC, AB, and BC.

15. Find the length of the missing segment Find MN if ◦LN = 20 ◦LM = 15 Find DS if ◦DT = 60 ◦DS = 2x – 8 ◦ST = 3x – 12 LM N 15 20 LM + MN = LN 15 + MN = 20 MN = 5 DS T 2x - 8 60 3x - 12 DS + ST = DT (2x - 8) + (3x -12) = 60 5x – 20 = 60 x = 16 DS = 2x – 8 DS = 2(16) – 8 DS = 24

16. Find the length of the missing segment Point B is between points A and C on a line. AC = 75, AB = x + 15, and BC = 5x Draw a picture and find AC, AB, and BC. X + 15 + 5x = 75AB = x + 15 = 10 + 15 = 25 6x + 15 = 75BC = 5x = 5(10) = 50 6x = 60AC = 25 + 50 = 75 X = 10 CBA 75 5xX + 15

17. Segment Addition postulate: a special case How many values did we just use in our equations to apply the SAP? There is a special case where we only need 2 values (2 parts or 1 part and 1 whole) – when the two parts are THE SAME This special case deals with a MIDPOINT, which BISECTS the segment or cuts it into two EQUAL parts

20. How far are you? You are running a race. The route is shown below. Can you figure out how far you are from the first aid station?

21. How far are you? Using the given information, determine how far you are from the first aid station. Challenge: XR = 5x + 6, RY = 3x, XS = 11x + 6. How far are you from the first aid station?

22. How far are you? What is the distance to a drink station located at the midpoint between your current location and the first aid station?

23. Check Your Understanding Complete the following table How is the SAP with Midpoint similar to and different from the general case of the Segment Addition Postulate?

24. Independent Practice

25. Closure In your own words, explain the main idea behind the Segment Addition Postulate. Using this main idea, why can we call this a “postulate”?

26. Life’s Work Add Segment Addition Postulate and midpoint to your Glossary. Complete Independent Practice Problems in your Guided Notes