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Math 1 2 3 4
10.4 Notes
For each word compare the examples with the counterexamples and write a definition.
1. POLYGON
EXAMPLES:
Define a POLYGON:
What do you think are some names of Polygons?
COUNTEREXAMPLES:
Prefix:
Meaning:
Tri-
three
Quad-
four
Penta-
five
Hexa-
six
Hepta-
seven
Octa-
eight
There can also be Polygons or Regular Polygons.
2. REGULAR POLYGON:
EXAMPLES:
Define a Regular Polygon
COUNTEREXAMPLES:
Finding the Sum of the Interior Angles in a regular polygon:
a. How many degrees in a triangle? ________
b. We need to take the polygon and divide it into triangles. You need to choose
one vertice, let’s say the top left, and use that vertice to draw diagonals to all
of the other vertices.
Example:
I chose the top left vertex and drew a line to every other vertex, but I was only able to
form 2 triangles.
If one triangle is 180 degrees, then 180 × 2 = 360 degrees
So the Sum of the Interior Angles of a square is 360 degrees.
c. Draw in the triangles for the pentagon below:
How many triangles did you draw?________
What is the sum of the interior angles of the pentagon?___________
d. Draw in the triangles for the hexagon below:
How many triangles did you draw?________
What is the sum of the interior angles of the hexagon?___________
e. Fill in the chart below with the data that you just acquired. Then if you see
a pattern, try to fill in the rest of the data for the heptagon and the octagon.
Polygon Shape
Number of sides
Number of triangles
that can be drawn
from one vertex to
the others
Sum of the interior angles
(multiply the # of
triangles in each shape by
180 degrees)
Triangle
Square
Pentagon
Hexagon
Heptagon
Octagon
f. If a polygon had 100 sides, could you come up with an equation to solve
the sum of the interior angles, based on a pattern that you saw in the chart
above?
g. If you knew that the sum of a hexagon’s interior angles were 720
degrees, can you figure out what ONE angle measures?
(hint: all angles are equal…right?)?
3. PARALLELOGRAMS:
EXAMPLES:
COUNTEREXAMPLES:
Define a Parallelogram
4. QUADRILATERALS VS. PARALLELOGRAMS:
QUADRILATERALS:
PARALLELOGRAMS:
a. After comparing the quadrilaterals to the parallelograms, what do they have
in common?
b. How are quadrilaterals and parallelograms different?
5. TRAPEZOIDS
EXAMPLE:
COUNTEREXAMPLES:
Define a Trapezoid
6. RHOMBUS
EXAMPLE:
Define a Rhombus
COUNTEREXAMPLES:
Classifying Polygons
Tell whether the figure is a polygon. If it is, classify it. If it is not, explain why not.
Tell whether the figure is a polygon. If it is, classify it. If it is not, explain why not.