Algebraic Poofs, Inductive & Deductive Reasoning

The type of reasoning where a person makes  conclusions based on observations and patterns is called...

• Inductive reasoning
• Deductive reasoning
• Conjecture
• Experiments

What is a conjecture?

• A statement believed to be true based on observations.
• An example which disproves an hypothesis.
• the performance of tricks that are seemingly magical

Complete the conjecture.  Think of examples to help.
The product of any two odd numbers is _____________

• even
• odd
• zero
• positive

What are the next two numbers in this pattern?
12, 17, 22, 27, ___, ___

• 32, 37
• 30, 37
• 30, 33
• 32, 35

Used to prove that a conjecture is false.

• Counterexample
• Inductive Reasoning
• Concluding statement
• Conjecture

The sum of the interior angle of a square is 360.

The sum of the interior angle of a rectangle is 360.

The sum of the interior angle of parallelogram is 360.

The sum of the interior angle of a rhombus is 360.

What is the possible conclusion base on the given information?

• The sum of the exterior angles of a quadrilateral is 360.

• The sum of the interior angles is 360.

• The sum of the interior angles of a quadrilateral is 360.

• The interior angle of a quadrilateral is 360.

Reasoning based on facts, definitions, accepted properties, and the laws of logic is called ____________ reasoning.

• Inductive

• Deductive

p→q p ∴q Which law is modeled? #37

• Law of Syllogism
• Law of Detachment
• Law of Contrapositive
• Law of Shannon

p→q q→r ∴p→r Which law is modeled? #32

• Law of Syllogism
• Law of Detachment
• Law of Contrapositive
• Law of Shannon

Use the Law of Syllogism to make a conclusion. If the perimeter of a square is 20 ft, then the length of a side is 5 ft. If the length of a side of a square is 5 ft, then the area is 25 ft². #39

• If the side of a square is 5 ft, then the perimeter is 20 ft.
• If the perimeter of a square is 20 ft, then the area is 25 ft²
• If the area of a square is 25 ft², then the side length is 5 ft. 
• If the are of a square is 25 ft², then the perimeter is 20 ft.