Warm-Up

1
Warm-Up

• Solve the equation below. Show each step.

2
Warm-Up

• Determine if statements follow the Law of
  Detachment or Law of Syllogism. If they follow
  one of these laws, use the given information to
  write a conclusion.
• If today is Sunday, then tomorrow is Monday.
• If tomorrow is Monday, then I need to do my
  homework
• If there is a teachers meeting, then you will be
  dismissed early.
• If tomorrow is Martin Luther King day, then you
  will have the day off.
• If the chess club meets today, then it is
  Thursday.
• Today is Thursday.
• If two angles are vertical angles, then they are
  congruent.
• Angle A and Angle B are vertical angles.

3
Section 2.5 Reasoning in Algebra and Geometry

• SWBAT use properties from Algebra and Geometry to
  justify arguments

4
Two Column Proofs The Basics
5
Suggestions

• You should state at least one of your givens in
  your first step
• Your last step should be what youd like to prove
• Write out EVERY step, assumption, idea.

6
Statements

•  

7
Reasons

• These are things that support you going from one
  statement to the next

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Defintions

• Congruent
• Two angles are congruent if and only if they are
  equal in size
• Complementary
• Two angles that add up to 90 degrees
• Supplementary
• Two angles that add up to 180 degrees
• Vertical Angles
• Angles whose rays form two lines
• Midpoint
• A point that is exactly in the middle (separates
  two equal halves)
• Bisect
• Cuts into two equal pieces

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Properties

• Transitive Property
• If ab and bc then ac
• Symmetric Property
• If xy then yx
• Reflexive Property
• a a, things are congruent to themselves
• Substitution Property
• If ab4 and a3, then 3b4

10
Properties

• Addition/Subtraction/Multplication/Division
  Property of Equality
• You can add/subtract/multiply/divide the same
  thing from each side of an equation and it will
  remain equal
• Important Note! If you plan on using one of
  these, you should first use the reflexive
  property!
• Distributive Property
• a(bc)ab ac

11
Example

• In the picture below, AB CD. Write an argument
  that shows AC BD

A
B
C
D
12
Homework

• P. 99 10-18E, 24-25, 28
• Note Any definitions that we know can also be
  used in proofs. Some examples include the
  definition of acute, right, obtuse,
  complementary, supplementary, perpendicular,
  parallel, collinear, etc.
• If you choose to use one of these the reasoning
  in the right hand column will be Definition of
  _______