Download 10-7

(page 446-449)
Indicator  G2: Properties of 2dimensional figures
The size and shape of each state in the
United States is different. Analyze the shapes
of the states in both groups below.
1
1
Group 1
Group 2
1- Utah
2-Florida
1-Wyoming
2-Texas
2
1
2
1
2
2
1-New Mexico 2-Indiana
1-Colorado
2- North
Carolina
What are the differences between
the shapes in the two groups?
• On the previous slide, the states from group
1 are polygons.
• A polygon is a simple, closed figure formed
by 3 or more straight lines.
• A simple figure does not have lines that
cross each other.
Polygons
• Line segments are sides
• Sides meet at endpoints
• Points of intersection are vertices
Not Polygons
• Sides overlap
• Figure is open
• Sides are curved
Polygons are classified by the
number of sides they have.
Words pentagon hexagon heptagon octagon nonagon decagon
Number
of sides
Models
5
6
7
8
9
10
• A polygon that has all sides congruent
and all angles congruent is called a
regular polygon.
• Equilateral triangles and squares are
examples of regular polygons.
Reminder: The sum of all angles
in a triangle is 180º and in a
quadrilateral is 360º.
To find the measure of the angles in
a regular polygon:
1.
2.
3.
Draw all the diagonals from ONE
vertex & count the number of
triangles. (Each Triangle= 180º)
Find the sum of the angle
measures in the polygon.
Find the measure of each angle
by dividing by the number of
angles.
1
2
3
3 Triangles
3 × 180º = 540º
5n = 540
5
5
n= 108
The measure of each angle in a regular pentagon is 108º.
Sides Triangles
Angle sum
Each angle ° of
regular polygon
3
1
1 x 180 = 180°
180/3 = 60°
4
2
2 x 180 = 360°
360/4 = 90°
5
3
3 x 180 = 540°
540/5 = 108°
6
N
One more thing…
• A tessellation is a pattern of
polygons that fit together with no overlaps
and no holes.
• The sum of the measures of the angles
where the vertices meet in a tessellation
90º
is 360º
135
135º
135º
135
+90
360º
Homework
• Page 449-450 #8-28 even, 32-45 all
• & Extra Credit Tessellation
– (Must be in color)