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**Sec 1-2 Concept: Using Segments and Congruence**

Obj: given the segment addition postulate, find the length of a segment as measured by a s.g.

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**Postulate 1: Ruler Postulate**

The distance between points A and B, written as AB, is the absolute value of the difference between the coordinates of A and B AB is also called the length of AB AB A B X2 x1 AB = l x2-x1 l

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**Example 1: A B Find the length of AB AB = l 2-(-3) l = l 5 l = 5 1 2 3**

1 2 3 -1 -2 -3 AB = l 2-(-3) l = l 5 l = 5

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**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. A B C

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**Their houses are 692 yds apart**

Example 2: Two friends leave their homes and walk in a straight line towards the other’s home. When they meet one has walked 425 yds and the other has walked 267 yds. How far apart are their homes? A B C 267 425 AB + BC = AC = AC 692 = AC Their houses are 692 yds apart

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**Example 3: In the diagram of collinear points, GK=24, HJ = 10, and GH=HI=IJ. Find each length**

JK = IG = IK = 5 5 5 9 10 14

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**Example 4: Suppose M is between L and N**

Example 4: Suppose M is between L and N. Use the segment addition postulate to solve for the variable. Then find the lengths of LM, MN and LN LM = 3x+8 MN = 2x-5 LN =23 LM = 7y +9 MN = 3y + 4 LN = 143 143 23 L M N L M N 7y+9 3y+4 3x+8 2x-5 (7y+9) + (3y+4) = 143 10y + 13 =143 10y = 130 y=13 (3x+8) + (2x-5) = 23 5x+3=23 5x=20 X=4 MN=3y+4 3(13)+4 43 LM = 3x+8 3(4)+8 20 MN = 2x-5 2(4)-5 3 LM=7y+9 7(13)+9 100

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**A(0,1), B(4,1), C(1,2), D(1,6); AB and CD?**

Example 5: Plot the given points in a coordinate plane. Then determine whether the line segments named are congruent. A(0,1), B(4,1), C(1,2), D(1,6); AB and CD? D AB = 4 CD=4 Yes they are congruent C A B

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Today’s Work In Class: Homework:

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Section 1.3 Segments & Their Measures 1/14. Geometric Vocabulary Postulate : Rules that are accepted without proof. Axiom : Synonym for postulate. Theorem.

Section 1.3 Segments & Their Measures 1/14. Geometric Vocabulary Postulate : Rules that are accepted without proof. Axiom : Synonym for postulate. Theorem.

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