Segments and Their Measures

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Presentation transcript:

Segments and Their Measures Chapter 1 Section 1.3 Segments and Their Measures

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

The Ruler Postulate Part 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 A B x1 x2 Coordinates

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 A B x1 x2 AB = |x2 – x1|

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.

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 A B C AB BC The whole length is the sum of the little lengths

Distance Formula Find AB (AB)2 = (x2 – x1)2 + (y2 – y1)2 • B (x2, y2) C(x2, y1) • A(x1, y1) |x2 – x1| |y2 – y1| 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

Draw a Sketch of three collinear points then write the segment addition postulate for the points A is between T and Q 5. M is between H and A 6. J is between S and H 7. A is between L and B

In Exercises 8-11, Use the Following Information. S Is Between T and 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 8. Find RS 9. Find QS

In Exercises 8-11, Use the Following Information. S Is Between T and 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

Suppose J is between H and K, use the segment addition postulate to solve for x then find the length of each segment H J K HJ = 2x + 4 JK = 3x + 3 KH = 22

Suppose J is between H and K, use the segment addition postulate to solve for x then find the length of each segment H J K HJ = 5x - 3 JK = 8x - 9 KH = 131

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

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