Measuring Segments and Coordinate Plane

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This slideshow was used to introduce application of Segment Addition Postulate along with Coordinate Plane in Geometry. There is a review of several concepts at the end of the two lessons.

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Measuring Segments and Coordinate Plane

  1. 1. 1.4: Measuring Segments and Angles<br />Prentice Hall Geometry<br />
  2. 2. C<br />E<br />A<br />B<br />D<br />0<br />-8<br />8<br />-2<br />-4<br />-1<br />2<br />4<br />6<br />-6<br />The numerical location of a point on a number line.<br />Coordinate :<br />On a number line length <br />AB = AB = |B - A|<br />Length :<br />On a number line, midpoint of <br />AB = 1/2 (B+A) <br />Midpoint :<br />
  3. 3. Find which two of the segments XY, ZY, and ZW are congruent. <br />Because XY = ZW, XYZW.<br />Measuring Segments and Angles<br />GEOMETRY LESSON 1-4<br />Find the length of each segment.<br />XY = | –5 – (–1)| = | –4| = 4<br />ZY = | 2 – (–1)| = |3| = 3<br />ZW = | 2 – 6| = |–4| = 4<br />
  4. 4. The Segment Addition Postulate<br />If three points A, B, and C are collinear and B is between A and C, then AB + BC = AC.<br />A<br />B<br />C<br />
  5. 5. AN = 2x – 6 = 2(8) – 6 = 10<br />NB = x + 7 = (8) + 7 = 15<br />Substitute 8 for x.<br />If AB = 25, find the value of x. Then find AN and NB.<br />Use the Segment Addition Postulate to write an equation.<br />AN + NB = ABSegment Addition Postulate<br />(2x – 6) + (x + 7) = 25 Substitute.<br />3x + 1 = 25 Simplify the left side.<br /> 3x = 24 Subtract 1 from each side.<br />x = 8 Divide each side by 3.<br />AN = 10 and NB = 15, which checks because the sum of the segment lengths equals 25.<br />
  6. 6. RM = 5x + 9 = 5(15) + 9 = 84 <br />MT = 8x – 36 = 8(15) – 36 = 84<br />Substitute 15 for x.<br />RM and MT are each 84, which is half of 168, the length of RT.<br />Mis the midpoint of RT. Find RM, MT, and RT.<br />Use the definition of midpoint to write an equation.<br />RM = MTDefinition of midpoint<br />5x + 9 = 8x – 36Substitute.<br />5x + 45 = 8xAdd 36 to each side.<br /> 45 = 3xSubtract 5x from each side.<br /> 15 = xDivide each side by 3.<br />RT = RM + MT= 168<br />
  7. 7. Quiz<br />1. T is in between of XZ. <br />If XT = 12 and XZ = 21, <br />then TZ = ?<br />2. T is the midpoint of XZ. <br />If XT = 2x +11 and XZ = 5x + 8, <br />find the value of x.<br />
  8. 8. Coordinate Plane<br />
  9. 9. Parts of Coordinate Plane<br />y-axis<br />Quadrant II<br />Quadrant I<br />( - , + )<br />( +, + )<br />origin<br />x-axis<br />Quadrant III<br />Quadrant IV<br />( - , - )<br />( + , - )<br />
  10. 10. Distance<br />On a number line<br /> formula: d = | x2 – x1 |<br />On a coordinate plane<br /> formula:<br />
  11. 11. Find the distance between T(5, 2) and R( -4. -1) to the nearest tenth.<br />
  12. 12. Midpoint<br />On a number line<br /> formula: <br />On a coordinate plane<br /> formula:<br />
  13. 13. The midpoint of AB is M(3, 4). <br />One endpoint is A(-3, -2). <br />Find the coordinates of the other endpoint B.<br />
  14. 14. <ul><li>Angles
  15. 15. Formed by two rays with the same endpoint.
  16. 16. The rays: sides
  17. 17. Common endpoint: the vertex
  18. 18. Name:
  19. 19. Measures exactly 90º
  20. 20. Measure is GREATER than 90º
  21. 21. Measure is LESS than 90º
  22. 22. Measure is exactly 180º ---this is a line
  23. 23. Angles with the same measure.
  24. 24. Right Angle
  25. 25. Obtuse Angle
  26. 26. Acute Angle
  27. 27. Straight Angle
  28. 28. Congruent Angles</li></ul>FAD , FBC, 1 <br />FAD<br />ADE <br />FAB <br />1<br />2<br />
  29. 29. Name the angle below in four ways.<br />The name can be the number between the sides of the angle: <br />The name can be the vertex of the angle: G.<br />Finally, the name can be a point on one side, the vertex, <br />and a point on the other side of the angle: <br />AGC,CGA.<br />3<br />
  30. 30. Suppose that m 1 = 42 and m ABC = 88. Find m 2.<br />Use the Angle Addition Postulate to solve.<br />m 1 + m 2 = m ABCAngle Addition Postulate.<br />42 + m 2 = 88Substitute 42 for m 1 and 88 for m ABC.<br />m 2 = 46 Subtract 42 from each side.<br />
  31. 31. Use the figure below for Exercises 1-3.<br />1. If XT = 12 and XZ = 21, then TZ = 7.<br />2. If XZ = 3x, XT = x + 3, and TZ = 13,<br /> find XZ.<br />3. Suppose that T is the midpoint of XZ.<br /> If XT = 2x + 11 and XZ = 5x + 8, <br /> find the value of x. <br />Use the figure below for Exercises 4–6.<br />4. Name 2 two different ways. <br />5. Measure and classify 1, 2, <br /> and BAC.<br />6. Which postulate relates the measures <br /> of 1, 2, and BAC?<br />9<br />24<br />DAB and BAD<br />90°, right; 30°, acute; 120°, obtuse<br />14<br />Angle Addition Postulate<br />
  32. 32. Homework<br />Page 56 # 2, 4, 18, 20, 24, 26<br />
  33. 33. REVIEW!<br />Page 71 # 1- 16<br />Page 72 # 19- 31<br />Page 73 # 34- 38<br />

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