Transcript Math 2A: [10-6] Polygons

Polygons
»A polygon is a simple, closed
figure formed by three or more
straight lines.
»Examples:
»Non-Examples:
»Polygons are named by the
number of sides they have.
3 Sides…
Triangle
4 Sides…
Quadrilateral
5 Sides…
Pentagon
6 Sides…
Hexagon
7 Sides…
Heptagon
8 Sides…
Octagon
9 Sides…
Nonagon
10 Sides…
Decagon
n Sides… n-gon Ex: 21-gon
»A polygon that has all sides and
angles congruent is called a
regular polygon.
»Classify each polygon and state whether
it is regular. If it is not a polygon,
explain why.
1. A quadrilateral is a closed
figure with four sides and four
angles.
1.
The
quadrilateral
6.
family tree:
2.
3.
4.
5.
2. A parallelogram is a
quadrilateral with two pair of
parallel sides.
3. A rectangle is a quadrilateral
with four right angles.
4. A rhombus is a quadrilateral
with 4 congruent sides.
5. A square is a quadrilateral with
4 right angles and 4 congruent
sides.
6. A trapezoid is a quadrilateral
with 1 pair of parallel sides.
1
2
3
4
•The sum of the angles in any
quadrilateral is always 360°.
• 1 + 2 + 3 + 4 = 360°
Find the missing angles.
45°
55°
118°
100°
x°
80°
50°
y°
»This formula can be used to find the
angle sum of any polygon:
A = 180(n − 2)
Angle
Number
Sum
of Sides
A = 180(n − 2)
Divide by
A = 180(4 − 2)
n to find
A = 180(2)
each angle.
A = 360°  4 = 90°
»Find the measure of each interior angle
in a regular octagon.
»Perimeter is the distance
around any polygon.
»What is the perimeter
of this regular pentagon?
2.4 m
5 × 2.4 = 12 m
»A repetitive pattern of polygons
that fit together with no overlaps
or holes is called a tessellation.
BW: [10-6] Review
»Find the measure of each interior angle,
round to the nearest tenth if necessary.
Regular
dodecagon
(12 sides)
Regular
undecagon
(11 sides)
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