Classify polygons

basic

1. 1

2. 2
Polygons

3. 3
These figures are not polygonsThese figures are polygons
Definition:A closed figure formed by line segments so that each
segment intersects exactly two others, but only at their
endpoints.
Polygons

4. 4
Classifications of a Polygon
Convex:No line containing a side of the polygon contains a point
in its interior
Concave:
A polygon for which there is a line
containing a side of the polygon and
a point in the interior of the polygon.

5. 5
Regular:A convex polygon in which all interior angles have the
same measure and all sides are the same length
Irregular:Two sides (or two interior angles) are not congruent.
Classifications of a Polygon

6. 6
Polygon Names
3 sides Triangle
4 sides
5 sides
6 sides
7 sides
8 sides
Nonagon
Octagon
Heptagon
Hexagon
Pentagon
Quadrilateral
10 sides
9 sides
12 sides
Decagon
Dodecagon
n sides n-gon

7. Regular Polygons
Regular polygons have:
•All side lengths congruent
•All angles congruent
7

8. Area of Regular Polygon
Apothem of a polygon: the distance from
the center to any side of the polygon.
8

9. Area of Regular Polygon
We can now subdivide the polygon into
triangles.
9
sidesofNumbern
apothema
lengthsides
nasArea
__
_
2
1
=
=
=
××=

10. 10
Triangles and Quadrilaterals

11. 11
Classifying Triangles by Sides
Equilateral:
Scalene:A triangle in which all 3 sides are different lengths.
Isosceles:A triangle in which at least 2 sides are equal.
A triangle in which all 3 sides are equal.
A
B
=
3
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2
c
m
A
C

=

3
.
1
5

c
m
BC = 3.55 cm
A
B
C
A
B
=
3 . 4 7 c m
A
C

=

3
.
4
7

c
m
BC = 5.16 cmB
C
A
HI = 3.70 cm
G
H I
GH = 3.70 cm
G
I

=

3
.
7
0

c
m

12. 12
Classifying Triangles by Angles
Acute:
Obtuse:
A triangle in which all 3 angles are less than 90˚.
A triangle in which one and only one
angle is greater than 90˚& less than 180˚
108°
44°
28°
B
C
A
57° 47°
76°
G
H I

13. 13
Classifying Triangles by Angles
Right:
Equiangular:
A triangle in which one and only one angle is 90˚
A triangle in which all 3 angles are the same measure.
34°
56°
90°
B C
A
60°
60°60°
C
B
A

14. 14
polygons
Classification by Sides
with Flow Charts & Venn Diagrams
triangles
Scalene
Equilateral
Isosceles
Triangle
Polygon
scalene
isosceles
equilateral

15. 15
polygons
Classification by Angles
with Flow Charts & Venn Diagrams
triangles
Right
Equiangular
Acute
Triangle
Polygon
right
acute
equiangular
Obtuse
obtuse

16. What is a Quadrilateral?
All quadrilaterals have four
sides.
They also have four angles.
The sum of the four angles
totals 360°
These properties are what
make quadrilaterals alike,
but what makes them
different?

17. Parallelogram
Two sets of parallel sides
Two sets of congruent sides.
The angles that are opposite
each other are congruent
(equal measure).

18. Rectangle
Has all properties of quadrilateral and
parallelogram
A rectangle also has four right angles.
A rectangle can be referred to as an
equiangular parallelogram because all
four of it’s angle are right, meaning they
are all 90° (four equal angles).

19. Rhombus
 A rhombus is sometimes referred to as a
“slanted square”.
 A rhombus has all the properties of a
quadrilateral and all the properties of a
parallelogram, in addition to other properties.
 A rhombus is often referred to as a
equilateral parallelogram, because it has four
sides that are congruent (each side length has
equal measure).


20. Square
The square is the most specific member of
the family of quadrilaterals. The square
has the largest number of properties.
Squares have all the properties of a
quadrilateral, all the properties of a
parallelogram, all the properties of a
rectangle, and all the properties of a
rhombus.
A square can be called a rectangle,
rhombus, or a parallelogram because it
has all of the properties specific to those
figures.

21. Trapezoid
Unlike a parallelogram,
rectangle, rhombus, and
square who all have two sets of
parallel sides, a trapezoid only
has one set of parallel sides.
These parallel sides are
opposite one another. The
other set of sides are non
parallel.

22. Isosceles Trapezoid
One can never assume a trapezoid is
isosceles unless they are given that the
trapezoid has specific properties of an
isosceles trapezoid.
Isosceles is defined as having two equal
sides. Therefore, an isosceles trapezoid has
two equal sides. These equal sides are
called the legs of the trapezoid, which are the
non-parallel sides of the trapezoid.
Both pair of base angles in an isosceles
trapezoid are also congruent.

23. Right Trapezoid
A right trapezoid also has one set of
parallel sides, and one set of non-
parallel sides.
A right trapezoid has exactly two right
angles. This means that two angles
measure 90°.
There should be no problem identifying
this quadrilateral correctly, because it’s
just like it’s name. When you think of
right trapezoid, think of right angles!

24. Quadrilateral Family Tree
It’s important to have a good
understanding of how each of the
quadrilaterals relate to one another.
Any quadrilateral that has two sets of
parallel sides can be considered a
parallelogram.
A rectangle and rhombus are both types
of parallelograms, and a square can be
considered a rectangle, rhombus, and a
parallelogram.
Any quadrilateral that has one set of
parallel sides is a trapezoid. Isosceles and
Right are two types of trapezoids.
Quadrilateral
Parallelogram Trapezoid
Rectangle Rhombus
Square
Isosceles
Trapezoid
Right
Trapezoid

25. 25
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