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1-2. Measuring and Constructing Segments. Warm Up. Lesson Presentation. Lesson Quiz. Holt Geometry. Are you ready? Simplify. 1. 7 – (–3) 2. –1 – (–13) 3. | –7 – 1| Solve each equation. 4. 2 x + 3 = 9 x – 11 5. 3 x = 4 x – 5 6. How many numbers are there between and ?.

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  1. 1-2 Measuring and Constructing Segments Warm Up Lesson Presentation Lesson Quiz Holt Geometry

  2. Are you ready? Simplify. 1.7 – (–3) 2. –1 – (–13) 3. |–7 – 1| Solve each equation. 4. 2x + 3 = 9x – 11 5. 3x = 4x – 5 6. How many numbers are there between and ?

  3. Objectives TSW use length and midpoint of a segment. TSW construct midpoints and congruent segments.

  4. When would I ever use this? You can measure a segment to calculate the distance between two locations. Maps of a race are used to show the distance between stations on the course.

  5. Vocabulary coordinate midpoint distance bisect length segment bisector construction between congruent segments

  6. A ruler can be used to measure the distance between two points. A coordinate is a point corresponds to one and only one number on a ruler.The following postulate summarizes this concept.

  7. The distance between any two points is the absolute value of the difference of the coordinates. If the coordinates of points A and B are a and b, then the distance between A and B is |a – b| or |b – a|. The distance between A and B is also called the length of AB, or AB. A B AB = |a – b| or |b - a| a b

  8. Example 1: Finding the Length of a Segment Find each length. A. BC B. AC

  9. Example 2 Find each length. b. XZ a. XY

  10. Congruent segments are segments that have the same length. In the diagram, PQ = RS, so you can write PQRS. This is read as “segment PQ is congruent to segment RS.” Tick marksare used in a figure to show congruent segments.

  11. You can make a sketch or measure and draw a segment. These may not be exact. A construction is a way of creating a figure that is precise.

  12. Constructing a Congruent Segment You will need a ruler and a compass.

  13. In order for you to say that a point B is between two points A and C, all three points must lie on the same line, and AB + BC = AC.

  14. Example 3: Using the Segment Addition Postulate G is between F and H, FG = 6, and FH = 11. Find GH.

  15. Example 3B: Using the Segment Addition Postulate M is between N and O. Find NO.

  16. Example 3c Y is between X and Z, XZ = 3, and XY = . Find YZ.

  17. Example 3d E is between D and F. Find DF.

  18. The midpointM of AB is the point that bisects, or divides, the segment into two congruent segments. If M is the midpoint of AB, then AM = MB. So if AB = 6, then AM = 3 and MB = 3.

  19. Example 4: Recreation Application The map shows the route for a race. You are 365m from drink station R and 2km from drink station S. The first-aid station is located at the midpoint of the two drink stations. How far are you from the first-aid station? What is the distance to a drink station located at the midpoint between your current location and the first aid station?

  20. B is the midpoint of AC , AB = 5x, and BC = 3x + 4. Find AB, BC and AC.

  21. D is the midpoint of EF, ED = 4x + 6, and DF = 7x – 9. Find ED, DF, and EF. Example 5: Using Midpoints to Find Lengths E D 4x + 6 F 7x – 9

  22. A segment bisector is any ray, segment, or line that intersects a segment at its midpoint. It divides the segment into two equal parts at its midpoint. Let’s construct one now.

  23. 2. S is the midpoint of TV, TS = 4x – 7, and SV = 5x – 15. Find TS, SV, and TV. Lesson Quiz: Part I 1. M is between N and O. MO = 15, and MN = 7.6. Find NO. 3. Sketch, draw, and construct a segment congruent to CD.

  24. Lesson Quiz: Part II 4.LH bisects GK at M. GM =2x + 6, and GK = 24.Find x. 5. Tell whether the statement below is sometimes, always, or never true. Support your answer with a sketch. If M is the midpoint of KL, then M, K, and L are collinear.

  25. 2. S is the midpoint of TV, TS = 4x – 7, and SV = 5x – 15. Find TS, SV, and TV. Lesson Quiz: Part I 1. M is between N and O. MO = 15, and MN = 7.6. Find NO. 22.6 25, 25, 50 3. Sketch, draw, and construct a segment congruent to CD. Check students' constructions

  26. K M L Lesson Quiz: Part II 4.LH bisects GK at M. GM =2x + 6, and GK = 24.Find x. 3 5. Tell whether the statement below is sometimes, always, or never true. Support your answer with a sketch. If M is the midpoint of KL, then M, K, and L are collinear. Always

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