Chapter 1 Section 1 3 Segments and Their

More Definitions • Postulate/Axiom – Rules that are accepted without proof • Example: The

The Ruler Postulate Part 1 • The points on a line can be matched

Ruler Postulate Part 2 • The distance between points A and B, is the

Ruler Postulate in a nut shell • You can use a ruler to find

Segment Addition Postulate • If B is between A and C, then AB +

Distance Formula • B (x 2, y 2) Find AB (AB)2 = (x 2

Draw a Sketch of three collinear points then write the segment addition postulate for

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

Suppose J is between H and K, use the segment addition postulate to solve

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

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

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Chapter 1 Section 1. 3 Segments and Their Measures

More Definitions • Postulate/Axiom – 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 Coordinates A B x 1 x 2

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 x 1 x 2 AB = |x 2 – x 1|

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

Distance Formula • B (x 2, y 2) Find AB (AB)2 = (x 2 – x 1)2 + (y 2 – y 1)2 |y 2 – y 1| A(x 1, y 1) • C(x 2, y 1) |x 2 – x 1| 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 4. 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. 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. 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 12. HJ = 2 x + 4 JK = 3 x + 3 KH = 22 J K

Suppose J is between H and K, use the segment addition postulate to solve for x then find the length of each segment H 13. HJ = 5 x - 3 JK = 8 x - 9 KH = 131 J K

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