angles of a polygon and inductive reasoning 3.5 and 3.6

Angles of a Polygon and Inductive Reasoning3.5 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 ReasoningRemember 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.