2'7 Proving Segment Relationships 102208

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2.7 Proving Segment Relationships 10/22/08

• Ruler Postulate
• - The points on any line or line segment can
  be paired with real numbers so that, given
  any two points A and B on a line, A
  corresponds to zero and B corresponds to
  a positive real number.

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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.

AB
BC
A
B
C
AC
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Proof with Segment Addition

• Prove the following.
• Given PQ RS
• Prove PR QS

P
Q
S
R
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• Statements
• PQ RS
• PQ QR QR RS
• PQ QR PRQR RS QS
• PR QS

• Reasons
• Given
• Addition Property
• Segment Addition Property
• Substitution

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Segment Congruence

• Congruence of segments is reflexive, symmetric,
  and transitive.
• Reflexive
• Symmetric
• Transitive

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Proof with Segment Congruence

• Prove the following.
• Given
• Prove

7

• Statements
• 1.
• 2.
• 3.
• 4.
• 5.

• Reasons
• Given
• Transitive Property
• Given
• Transitive Property
• Symmetric Property

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HOMEWORK

• Study Guide 2.7