Download Angles of a Polygon and Inductive Reasoning

Angles of a
Polygon and
Inductive
Reasoning
3.5 AND 3.6
What is a polygon?
How do you know if it’s a polygon?
What do we call them??
Number of Sides
Name
3
Triangle
4
Quadrilateral
5
Pentagon
6
Hexagon
8
Octagon
10
Decagon
n
N-gon
A segment joining two non-consecutive
vertices is a diagonal of the polygon.
Theorem: The sum of the measures of the angles of a
convex polygon with n sides is (n-2)180.
Theorem: The sum of the measures of the
exterior angles of any convex polygon, one
angle at each vertex is 360.
If a polygon is both equiangular
and equilateral, it is called a regular
polygon.
Section 3.6: Inductive Reasoning
Remember deductive reasoning? A.K.A. If-Then statements,
biconditionals, etc.
Deductive Reasoning
Inductive Reasoning
Conclusion based on accepted
statements (definitions, postulates,
previous theorems, corollaries, and
given info)
Conclusion based on several past
observations
Conclusion MUST be true if hypotheses
are true
Conclusion is PROBABLY true, but not
necessarily true
Deductive or Inductive?
• Ramon noticed that spaghetti had been on the school menu for
the past five Wednesdays. Ramon decides that the school always
serves spaghetti on Wednesday.
• The next number in this pattern: 6, 12, 24, ______ should be 48.
• Ky did his assignment, adding the lengths of the sides of triangles
to find the perimeters. Noticing the results for several equilateral
triangles, he guesses that the perimeter of every equilateral
triangle is three times the length of a side.
• By using the definitions of equilateral triangles, and the definition
of perimeter, Katie concludes that the perimeter of every
equilateral triangle is three times the length of a side.