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6.1 Polygons
Week 1 Day 2
January 7th 2014
Warm UP: Identifying Polygons
• State whether the
figure is a polygon. If it
is not, explain why.
A
C
B
F
E
D
Essential Question :
• What is a polygon? How do we identify and
classify polygons? How do we find angle
measures of quadrilaterals?
Vocabulary
•
•
•
•
•
Polygon
Sides
Vertex of a polygon
Consecutive vertices
Diagonal of a polygon
Definitions
• A polygon is a plane figure that is
side
formed by three or more segments
called sides. (a closed, sided figure)
• Each side intersects exactly two other
sides at each of its endpoints. Each
endpoint is a vertex of the polygon.
• Two vertices that are endpoints of the
same side are consecutive vertices.
• A segment that joins two
nonconsecutive vertices of a polygon
diagonal
is called a diagonal.
Vertices
Consecutive vertices
Warm UP: Identifying Polygons
• State whether the figure
is a polygon. If it is not,
explain why.
• Not D – has a side that
isn’t a segment – it’s an
arc.
• Not E– because two of
the sides intersect only
one other side.
• Not F because some of its
sides intersect more than
two sides.
A
C
B
F
E
D
Figures A, B, and C are
polygons.
Polygons are named by the number of sides they have.
Fill in the blank.
Number of sides
Type of polygon
3
Triangle
4
Quadrilateral
5
Pentagon
6
Hexagon
7
Heptagon
8
Octagon
Quadrilateral Interior Angles Theorem
• The sum of the measures of the interior
angles of a quadrilateral is 360°.
B
m<A + m<B + m<C + m<D = 360°
C
A
D
Example
• Find m<Q and m<R.
x + 2x + 70° + 80° = 360°
3x + 150 ° = 360 °
3x = 210 °
x = 70 °
Q
x
R
m< Q = x
m< Q = 70 °
2x°
80° P
70°
S
m<R = 2x
m<R = 2(70°)
m<R = 140 °
Homework
• Page 306 # 8-10, 16, 18