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• Deductive reasoning uses facts,
definitions, and accepted properties in a
logical order to write a logical argument.
• Inductive reasoning uses previous
examples, observations and patterns to
make a conjecture.
Examples of Inductive Reasoning
1) Every quiz has been easy.
Therefore, the test will be easy.
2) Every fall there have been hurricanes
in the tropics. Therefore, there will be
hurricanes in the tropics this coming fall.
Example of Deductive Reasoning
The catalog states that all entering
freshmen must take a mathematics
placement test.
Conclusion: You will have to take a
mathematics placement test.
You are an entering freshman.
An Example:
Deductive reasoning is when you start from things you assume to be
true , and draw conclusions that must be true if your assumptions are
true.
Conditional Statement
• A logical statement with 2 parts
• Hypothesis is the part after the word “If”
• Conclusion is the part after the word
“then”
If _____________, then____________.
hypothesis conclusion
Ex: Underline the hypothesis &
circle the conclusion.
- If you are a brunette, then you have brown hair.
hypothesis conclusion
Ex: Underline the hypothesis &
circle the conclusion.
st
, then it is Halloween.
hypothesis conclusion
• To prove that a conjecture is true, you
need to prove it is true in all cases.
• To prove that a conjecture is false, you
need to provide a single counter example.
• A counterexample is an example that
shows a conjecture is false.
Solve the equation 4 m – 8 = – 12. Write a
justification for each step.
Example 1A: Solving an Equation in Algebra
4 m – 8 = – 12 Given equation
+8 +8 Addition Property of Equality
m = – 1
Division Property of Equality
Example 1C: Writing Reasons
Solve 5x – 18 = 3x +
1. 5x – 18 = 3x + 2
2. 2x – 18 = 2
3. 2x = 20
4. x = 10
1. Given
- Subtraction property
- Addition property
- Division property
Two angles that share a common side and a common vertex
Complementary Angles
Two angles are complementary angles if their sum is 90
o
.
Each angle is the complement of the other.
Note: the two complementary angles are not necessarily
adjacent angles.
complementary
adjacent
complementary
nonadjacent
Supplementary Angles
Two angles are supplementary angles if their sum is 180
o
Each angle is the supplement of the other.
Note: the two supplementary angles do not have to be
linear pair, BUT a linear pair must be supplementary.
supplementary
adjacent
supplementary
nonadjacent
