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Friday, August 8th

Friday, August 8th. Complete warm up on separate sheet of paper 1. 2 x + 3 = 9 x – 11 2. 3 x = 4 x – 5. What to do if you miss class?. Website. mskristaevans.wordpress.com Schedule Syllabus Homework Lessons. Binders/Notebooks. 5 Tabs for 5 Units

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Friday, August 8th

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  1. Friday, August 8th Complete warm up on separate sheet of paper 1. 2x+ 3 = 9x – 112. 3x= 4x – 5

  2. What to do if you miss class?

  3. Website mskristaevans.wordpress.com • Schedule • Syllabus • Homework • Lessons

  4. Binders/Notebooks • 5 Tabs for 5 Units • Label Unit 1, Unit 2, etc…. • You will need lots of lose leaf paper!

  5. Constructions

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

  7. Do we know how to use a protractor?! • Find the degrees of all 10 angles! • Make sure the you line up your protractor correctly 

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

  9. 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

  10. Example 1: Finding the Length of a Segment Find each length. A. BC B. AC BC = |1 – 3| AC = |–2 – 3| = |1 – 3| = |– 5| = 2 = 5

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

  12. 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 marks are used in a figure to show congruent segments.

  13. 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 more precise. One way to make a geometric construction is to use a compass and straightedge.

  14. Steps for constructioningA Line

  15. Sketch, draw, and construct a segment congruent to MN. Sketch: Estimate and sketch. Estimate the length of MN and sketch PQ approximately the same length. P Q Sketch, draw, and construct segment

  16. Sketch, draw, and construct a segment congruent to MN. Draw: Measure and draw. Use a ruler to measure MN. MN appears to be 3.5 in. Use a ruler to draw XY to have length 3.5 in. X Y Example 2 Continued

  17. Sketch, draw, and construct a segment congruent to MN. A ruler shows that PQ and XY are approximately the same length as MN, but ST is precisely the same length. Example 2 Continued Construct. Construct and compare. Use a compass and straightedge to construct ST congruent to MN.

  18. Sketch, draw, and construct a segment congruent to JK. Sketch. Estimate and sketch. Estimate the length of JK and sketch PQ approximately the same length. \Example 2

  19. Sketch, draw, and construct a segment congruent to JK. Draw: Measure and draw. Use a ruler to measure JK. JK appears to be 1.7 in. Use a ruler to draw XY to have length 1.7 in. Check It Out! Example 2 Continued

  20. Sketch, draw, and construct a segment congruent to JK. A ruler shows that PQ and XY are approximately the same length as JK, but ST is precisely the same length. Check It Out! Example 2 Continued Construct Constructand compare. Use a compass and straightedge to construct ST congruent to JK.

  21. 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.

  22. – 6 –6 Example 3A: Using the Segment Addition Postulate G is between F and H, FG = 6, and FH = 11. Find GH. FH = FG + GH Seg. Add. Postulate 11= 6 + GH Substitute 6 for FG and 11 for FH. Subtract 6 from both sides. 5 = GH Simplify.

  23. – 2 – 2 –3x –3x 2 2 Example 3B: Using the Segment Addition Postulate M is between N and O. Find NO. NM + MO = NO Seg. Add. Postulate 17 + (3x – 5) = 5x + 2 Substitute the given values 3x + 12 = 5x + 2 Simplify. Subtract 2 from both sides. Simplify. 3x + 10 = 5x Subtract 3x from both sides. 10 = 2x Divide both sides by 2. 5 = x

  24. Example 3B Continued M is between N and O. Find NO. NO = 5x + 2 = 5(5) + 2 Substitute 5 for x. Simplify. = 27

  25. Subtract from both sides. Check It Out! Example 3a Y is between X and Z, XZ = 3, and XY = . Find YZ. XZ = XY + YZ Seg. Add. Postulate Substitute the given values.

  26. – 3x – 3x 12 3x = 3 3 Check It Out! Example 3b E is between D and F. Find DF. DE + EF = DF Seg. Add. Postulate (3x – 1) + 13 = 6x Substitute the given values 3x + 12 = 6x Subtract 3x from both sides. Simplify. 12 = 3x Divide both sides by 3. 4 = x

  27. Check It Out! Example 3b Continued E is between D and F. Find DF. DF = 6x = 6(4) Substitute 4 for x. Simplify. = 24

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