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1.4: Measuring Segments and Angles Prentice Hall Geometry
C E A B D 0 -8 8 -2 -4 -1 2 4 6 -6 The numerical location of a point on a number line. Coordinate : On a number line length  AB = AB =  |B - A| Length : On a number line, midpoint of  AB = 1/2 (B+A)  Midpoint :
Find which two of the segments XY, ZY, and ZW are congruent.  Because XY = ZW,  XYZW. Measuring Segments and Angles GEOMETRY  LESSON 1-4 Find the length of each segment. XY = | –5 – (–1)| = | –4| = 4 ZY = | 2 – (–1)| = |3| = 3 ZW = | 2 – 6| = |–4| = 4
The Segment Addition Postulate If three points A, B, and C are collinear and B is between A and C, then AB + BC = AC. A B C
AN = 2x – 6 = 2(8) – 6 = 10 NB = x + 7 = (8) + 7 = 15 Substitute 8 for x. If AB = 25, find the value of x. Then find AN and NB. Use the Segment Addition Postulate to write an equation. AN + NB = ABSegment Addition Postulate (2x – 6) + (x + 7) = 25	  Substitute. 3x + 1 = 25	Simplify the left side.       3x = 24	Subtract 1 from each side. x = 8	Divide each side by 3. AN = 10 and NB = 15, which checks because the sum of the segment lengths equals 25.
RM = 5x + 9 = 5(15) + 9 = 84	 MT = 8x – 36 = 8(15) – 36 = 84 Substitute 15 for x. RM and MT are each 84, which is half of 168, the length of RT. Mis the midpoint of RT. Find RM, MT, and RT. Use the definition of midpoint to write an equation. RM = MTDefinition of midpoint 5x + 9 = 8x – 36Substitute. 5x + 45 = 8xAdd 36 to each side.       45 = 3xSubtract 5x from each side.         15 = xDivide each side by 3. RT = RM + MT= 168
Quiz 1. T is in between of XZ.  If XT = 12 and XZ = 21,  then TZ = ? 2. T is the midpoint of XZ.  If XT = 2x +11 and XZ = 5x + 8,  find the value of x.
Coordinate Plane
Parts of Coordinate Plane y-axis Quadrant II Quadrant I ( - , + ) ( +, + ) origin x-axis Quadrant III Quadrant IV ( - , - ) ( + , - )
Distance On a number line 		formula: d = | x2 – x1 | On a coordinate plane 		formula:
Find the distance between T(5, 2) and R( -4. -1) to the nearest tenth.
Midpoint On a number line 		formula:  On a coordinate plane 	formula:
The midpoint of AB is M(3, 4).  One endpoint is A(-3, -2).  Find the coordinates of the other endpoint B.
[object Object]
Formed by two rays with the same endpoint.
The rays: sides
Common endpoint: the vertex
Name:
Measures exactly 90º

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Measuring Segments and Coordinate Plane

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