Section 1.3Segments & Their

Measures

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Geometric Vocabulary

Postulate: Rules that are accepted without proof.

Axiom: Synonym for postulate.

Theorem: Rules that are proved.

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Geometric Notation

R B

Refers to the NAME of the object (the segment)

RBRB

Refers to the MEASUREMENT of the object (length of the segment)

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Segment Addition Postulate

If B is between A & C, then AB + BC = AC.

If AB + BC = AC, then B is between A & C.

A BC

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Segment Addition PostulateExample #1

A BC

AB = 15 cm

BC = x cm

AC = 41 cm

What is the value of x?

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Segment Addition PostulateExample #2

A BC

AB = x + 5 cm

BC = 2x cm

AC = 29 cm

What is the value of x?

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Segment Addition PostulateExample #3

A BC

AB = x + 10 cm

BC = 24 cm

AC = 3x - 2 cm

What is the length of AB?

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Segment Addition PostulateExample #4

A BC

AB = cm

BC = cm

AC = 18 cm What is the value of x?

1

3x

18

2x

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Where does the Distance Formula come from?

a

bc

2 2( , )x y

1 1( , )x y 2 1( , )x y

2 1( )x x

2 1( )y y

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Distance Formula

2 22 1 2 1( ) ( )AB x x y y

2 2c a b

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Distance Formula

2 22 1 2 1( ) ( )AB x x y y

Find the length of segment AB if the coordinates are E(-3, 3) and F(1, 6).

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Distance Formula

Find the length of segment GH if the coordinates are G(4, -3) and H(-1, 9).

2 22 1 2 1( ) ( )AB x x y y

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Congruent Segments

Congruent Segments: segments that have the same length.

If , then .

If , then .

AB CD

AB CD AB CD

AB CD AB CD

A B

C D

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Homework 1.3

P. 21 4 – 6, 10, 23 – 33, 56

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