Day 6 Problems 91208

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Day 6 Problems 9/12/08

• Identify the hypothesis and conclusion of the
  if-then statement.
• If the car is running, then the key is in the
  ignition.
• If the measure of an angle is 60, then the
  measure is acute.
• Rewrite the statement as an if-then statement.
• A number divisible by 6 is also divisible by 3
  and 2.
• Using the Law of Detachment, what can you
  conclude from the given true statement?
• If two planes intersect, then their intersection
  is a line. Two planes are intersecting.
• Using the law of syllogism, write the if-then
  statement that follows from the pair of true
  statements.
• 5. If the sun is shining, then it is a beautiful
  day. If it is a beautiful day, then we will have
  a picnic.

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Review!

• Textbook p. 98 1, 2, 5 13, p. 99 1, 3
  6, 8

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2.6 Properties of Equality and Congruence
9/12/08

• Properties of Equality and Congruence
• Reflexive property
• Symmetric Property
• Transitive Property

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Reflexive Property

• Equality Congruence
• AB AB AB AB
• m A m A A A

5
Symmetric Property

• Equality Congruence
• If AB CD, then CD AB If AB CD, then CD
  AB.
• If m A m B, then If A B,
  then
• m B m A. B A.

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Transitive Property

• Equality Congruence
• If AB CD and CDEF, If AB CD and CD EF
• then AB EF. then AB EF.
• If m A m B and If A B and
  B C,
• m B m C then then A C
• m A m C

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Properties of Equality

• Addition Property adding the same number to
  each side of an equation produces an equivalent
  equation.
• ex. x 3 7
• x 3 3 7 3
• Subtraction Property subtracting the same
  number from each side of an equation produces an
  equivalent equation.
• Ex. y 5 11
• y 5 5 11 - 5

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Properties of Equality (cont.)

• Multiplication Property multiplying each side
  of an equivalent by the same nonzero number
  produces an equivalent equation.
• ex. z 6
• z 6 4

1 4
1 4
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Properties of Equality (Cont.)

• Division Property dividing each side to an
  equation by the same nonzero number procedures an
  equivalent equation.
• ex. 8x 16
• 8x 16
• 8 8
• Substitution Property substituing a number for
  a variable in an equation procedures an
  equivalent
• ex. x 7
• 2x 4 2 (7) 4

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More Practice!!!

• Textbooks p. 91 1 15
• Homework worksheet 2.6