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Geometry Postulates and Formulas for Segments

Learn about postulates and formulas for measuring line segments, along with practical examples and exercises to enhance your understanding of geometric concepts.

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Geometry Postulates and Formulas for Segments

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  1. Chapter 1Section 1.3 Segments and Their Measures

  2. More Definitions • Postulate/Axiom • Rules that are accepted without proof • Example: The sun rise postulate • Tomorrow the sun will rise in the east.

  3. B A x2 x1 The Ruler PostulatePart 1 • The points on a line can be matched one to one with the real numbers. • The real number that corresponds to a point is called the coordinate of the point Name of points Coordinates

  4. B A x2 x1 Ruler Postulate Part 2 • The distance between points A and B, is the absolute value of the difference between the coordinates of A and B • The length of is denoted by AB AB = |x2 – x1|

  5. Ruler Postulate in a nut shell • You can use a ruler to find the coordinates of points on a line. • You can subtract the coordinates of points on a line to find the distance between them.

  6. B A C Segment Addition Postulate • If B is between A and C, then AB + BC = AC • If AB + BC = AC, then B is between A and C AC BC AB The whole length is the sum of the little lengths

  7. B (x2, y2) • |y2 – y1| • C(x2, y1) A(x1, y1) |x2 – x1| Distance Formula Find AB (AB)2 = (x2 – x1)2 + (y2 – y1)2 This formula can be used to find the distance between any two points in the plane

  8. Draw a Sketch of three collinear points then write the segment addition postulate for the points • A is between T and Q A T Q TA + AQ = TQ M H A 5.M is between H and A HM + MA = HA J S H 6.J is between S and H SJ + JH = SH A L B 7.A is between L and B LA + AB = LB

  9. In Exercises 8-11, Use the Following Information. S Is Between T and V. R Is Between S and T. T Is Between R and Q. QV = 18, QT = 6, and TR = RS = SV S T Q R V 8. Find RS 9. Find QS QV = QT + TR + RS + SV 18 = 6 + RS + RS + RS 12 = 3 RS 4 = RS QS = QT + TR + RS QS = 6 + 4 + 4 QS = 14

  10. S T Q R V In Exercises 8-11, Use the Following Information. S Is Between T and V. R Is Between S and T. T Is Between R and Q. QV = 18, QT = 6, and TR = RS = SV 10. Find TS 11. Find TV TS = TR + RS TS = 4 + 4 TS = 8 TV = TR + RS + SV TV = 4 + 4 + 4 TV = 12

  11. Suppose J is between H and K, use the segment addition postulate to solve for x then find the length of each segment J H K • HJ = 2x + 4 • JK = 3x + 3 • KH = 22 HJ + JK = HK 2x + 4 + 3x + 3 = 22 5x + 7 = 22 5x = 15 x = 3 HJ = 2(3) + 4 = 10 JK = 3(3) + 3 = 12

  12. J H K Suppose J is between H and K, use the segment addition postulate to solve for x then find the length of each segment • HJ = 5x - 3 • JK = 8x - 9 • KH = 131 HJ + JK = HK 5x - 3 + 8x - 9 = 131 13x - 12 = 131 13x = 143 x = 11 HJ = 5(11) – 3 = 52 JK = 8(11) - 9 = 79

  13. Find the distance between each pair of points 15. D(1, 3), E(-2, 4), F(0, -4) Find ED Find DF Find EF

  14. Find the distance between each pair of points 16. G(-1, 0), H(2, -4), I(1, 3) Find GH Find GI Find HI

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