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1-4: Segments & their Measures

1-4: Segments & their Measures. p. 28-35. Example : Find the measure of AB. A. B. Point A is at 1.5 and B is at 5. So, AB = 5 - 1 . 5 = 3.5. Example . Find the measure of PR Ans: |3-(-4)|=|3+4|=7 Would it matter if I asked for the distance from R to P ?.

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1-4: Segments & their Measures

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  1. 1-4: Segments & their Measures p. 28-35

  2. Example:Findthe measure of AB. A B Point A is at 1.5 and B is at 5. So, AB = 5 - 1.5 = 3.5

  3. Example • Find the measure of PR • Ans: |3-(-4)|=|3+4|=7 • Would it matter if I asked for the distance from R to P ?

  4. Is Alex between Ty and Josh? Yes! In order for a point to be between 2 others, all 3 points MUST BE collinear!! Ty Alex Josh No, but why not? How about now?

  5. What is a Postulate? • Rules that are accepted as true without having to be proven. • Sometimes they are called axioms.

  6. Post. 2: Segment Addition Post. • If B is between A & C, then AB + BC = AC. • If AB + BC = AC, then B is between A & C. C B A

  7. Seg. Add. Post. Example • If J is between H and K and HJ=5x-3 , JK = 4x, HK = 8x, find HJ, JK, HK • Ans: Draw a diagram

  8. Example • M is between L and N. Find each measurement if: LM = 4x+6 , LN = 5x+10 MN = 3x – 4 LM + MN = LN LM =4(4)+6 = 22 MN = 3(4)-4 = 8 LN = 5(4)+10 = 30

  9. Ex: if DE=2, EF=5, and DE=FG, find FG, DF, DG, & EG. D E F G FG=2 DF=7 DG=9 EG=7

  10. Ways to find the length of a segment on the coordinate plane • 1) Distance Formula – only used on the coordinate plane • 2) Pythagorean Theorem- Can be used on and off the coordinate plane

  11. 1) Distance Formula J (-3,5) T (4,2) J (-3,5) T (4,2) J (-3,5) T (4,2) x1, y1 x2, y2 Identify one as the 1st point and one as the 2nd. Use the corresponding x and y values Identify one as the 1st point and one as the 2nd. Use the corresponding x and y values Identify one as the 1st point and one as the 2nd. Use the corresponding x and y values Identify one as the 1st point and one as the 2nd. Use the corresponding x and y values (4-(-3))2 + (2-(5))2 (4+3)2 + (2-5)2 (7)2 +(-3)2 58 49+9 ~ = 7.6 ~

  12. Example of the Distance Formula • Find the length of the green segment Ans: 109 or approximately 10.44

  13. 2) Pythagorean Theorem* * Only can be used with Right Triangles What are the parts to a RIGHT Triangle? • Right angle • 2 legs • Hypotenuse Hypotenuse- Side across from the right angle. Always the longest side of a right triangle. LEG Right angle Leg – Sides attached to the Right angle

  14. 2) Pythagorean Theorem*

  15. Example of Pyth. Th. on the Coordinate Plane Make a right Triangle out of the segment (either way) Find the lengths of the legs by using the Distance Formula or counting if possible Use Leg 2 + Leg 2 = Hyp 2

  16. Find the length of CD using the Pythagorean Theorem 10 8

  17. Ex. Pythagorean Theorem off the Coordinate Plane • Find the missing segment- Identify the parts of the triangle Leg 5 in Leg2 + Leg2 = Hyp2 Ans: 52 + X2 = 132 Leg 13 in 25 + X 2 = 169 hyp X 2 = 144 X = 12 in

  18. ( ) Congruent Segments • Segments that have the same length. If AB & XY have the same length, Then AB=XY, but AB XY Symbolfor congruent

  19. Assignment

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