Geometry Drill 1/24/13 Pick up a paper and use your
protractor to find the sum of the interior angles of the polygons that have a check next them.
Write down the sum and the number of sides
Geometry Drill 1/24/13 1. What is the sum of the
angles of a triangle? 2. What is the sum of the
angles of a square?
Objective:
To determine the interior and exterior angle sum in any polygon.
To determine the measure of one interior & one exterior angle of a regular polygon.
POLYGON......1.A CLOSED PLANE FIGURE
2. EACH SEGMENT INTERSECTS EXACTLY TWO OTHER SEGMENTS ONE AT EACH ENDPOINT.
3. MADE OF 3 OR MORE SEGMENTS
WHICH ARE POLYGONS?
Convex or Concave Polygons ?
Convex Polygons
CONVEX POLYGONA polygon in which any line
segment connecting two points has no part outside the polygon.
CONVEX POLYGON.
Sides Interior Angle Sum
3 180
4 360
5 540
6 720
7 900
8 1080
9 1260
10 1440
n
Conjecture/Formula The sum of the measures of the angles of a convex polygon with n sides is _ .
Conjecture/Formula The sum of the measures of the angles of a convex polygon with n sides is 180(n–2) _ .
How many exterior angles are in the drawing?
CD
E
exterior angles
E
D C
10 exterior angles
E
D C
We will only be interested in ONE AT A VERTEX
E
D C
Conjecture/ Formula The sum of the measures
of the exterior angles of any convex polygon, one at each vertex is _____.
Conjecture/ Formula The sum of the measures
of the exterior angles of any convex polygon, one at each vertex is 360º.
Regular Polygon
A polygon with all sides and angles congruent.
Conjecture/Formula The measure of one interior
angle of any regular convex polygon is _____.
Conjecture/Formula The measure of one interior
angle of any regular convex polygon is
180(n–2)
n
Conjecture/Formula The measure of one
exterior angle of any regular convex polygon is _____.
Conjecture/Formula The measure of one
exterior angle of any regular convex polygon is 360º
n