1.3 Segments

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1.3 Segments their Measures
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Standard 8

• Students will have a foundation in geometric
  concepts.

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Postulates

• Rules that are accepted as true with having to be
  proven.
• Sometimes they are called axioms.

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Postulate 1 Ruler post.

• The points on a line can be matched with those on
  the real line.
• The real that corresponds to a point is the
  coordinate of the point.
• If you find the difference between the
  coordinates of 2 points, then take the absolute
  value, you will have the distance between the
  points.

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Ruler post. (continued)
A
B
x1
x2

• The length of AB can be found by x2 - x1
• The symbol for the length of AB is AB.

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Example Find AB.
A
B
Point A is at 1.5 and B is at 5. So, AB 5 -
1.5 3.5
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Is Alex between Ty and Josh?
Yes!
Ty
Alex
Josh
No, but why not?
How about now?

• In order for a point to be between 2 others, all
  3 points MUST BE collinear!!

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Post. 2 Segment Addition Post.

• If B is between A C, then
• AB BC AC.
• If AB BC AC, then B is between A C.

C
B
A
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Ex if DE2, EF5, and DEFG, find FG, DF, DG,
EG.
D
E
F
G
FG2 DF7 DG9 EG7
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Reminders

• Pythagorean Theorem
• a2b2c2
• a b are the lengths of the legs of a right
  triangle and c is the length of the hypotenuse.
• Distance formula
• (x1,y1) (x2,y2) are the 2 points.

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Congruent ( ) Segments

• Segments that have the same length.
• If AB XY have the same length,
• Then ABXY,
• but
• AB XY

Symbol for congruent