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1-5 Measuring Segments

• Find the distance between two points using the Ruler Postulate

• Determine the length of a segment using the Segment Addition Postulate

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Finding Segment Lengths• Simulation for measuring segments or hands-

on measuring activity with “broken” ruler• http://www.geogebra.org/en/upload/files/english/duane_habecker/broken_cm_ruler.html

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Ruler Postulate

•Given two points, the two points can be paired one to one with two real numbers.

•The real numbers are called the coordinates of the points

•To find the distance between the two points, subtract the coordinates; then take the absolute value (to ensure a positive distance)

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Example 1

• Find DE (distance between D and E)

-3 -1-2 10-8 2-7 -5-6 -4

D E

DE = | 0 – (2) | = | -2 | = 2

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Example 2

• Find AB (distance between A and B)

-3 -1-2 10-8 2-7 -5-6 -4

BA

AB = | -8 – (-5) | = | -3 | = 3

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Example 3

-3 -1-2 10-8 2-7 -5-6 -4

D EBA C

• Find BC (distance between B and C)

BC = | -5 – (-2) | = | -3 | = 3

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Example 4

-3 -1-2 10-8 2-7 -5-6 -4

D EBA C

AB = | -8 – (-5) | = | -3 | = 3BC = | -5 – (-2) | = | -3 | = 3

So AB = BC and

AB ≅ BC (Congruence of

segments)

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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

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Example 1

P Q S TFind ST.

QS + ST = QT

ST = QT – QS

ST = 12 – 8 = 4

QT = 12

QS = 8

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Example 2

DS + ST = DT

2x – 8 + 3x – 12 = 60

5x – 20 = 60

5x = 80

x = 16

DS = 2x – 8 = 2(16) – 8 = 24

ST = 3x – 12 = 3(16) – 12 = 36

D S TST = 3x – 12

DT = 60. Find x, DS, and ST

DS = 2x – 8

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Midpoint of a Segment

• A midpoint of a segment divides the segment into two congruent segments.

• The two marks indicate that the two segments are congruent.

AB BC≅

C

A

B

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Using the Midpoint

• AC = CB• 2x + 1 = 3x – 4• 1 = x – 4• 5 = x• AC = 2x + 1 = 2(5) + 1 = 11• CB = AC = 11• AB = AC + CB = 11 + 11 = 22

A C B

2x + 1 3x – 4

Given: C is the midpoint of AB. Find AC, CB, and AB.

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Learning Check and Summary

• Suppose X, Y, and Z are collinear. If XY = 10 and XZ = 6 and YZ = 4, which point lies between the other two points?

• The midpoint of a segments splits the segment into two ___?___ segments

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Homework

• Workbook 1-5 pp. 257-258