classify polygons
TRANSCRIPT
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Polygons
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These figures are not polygons These 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
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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.
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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
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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
Dodecagonn sides n-gon
Regular Polygons
Regular polygons have:• All side lengths congruent
• All angles congruent
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Area of Regular Polygon
Apothem of a polygon: the distance from the center to any side of the polygon.
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Area of Regular Polygon
We can now subdivide the polygon into triangles.
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sidesofNumbern
apothema
lengthsides
nasArea
__
_2
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Triangles and Quadrilaterals
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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.
AB
= 3
.02
cm
AC
= 3.15 cm
BC = 3.55 cm
A
B CAB =
3.47
cmAC = 3.47 cm
BC = 5.16 cmBC
A
HI = 3.70 cm
G
H I
GH = 3.70 cm
GI = 3.70 cm
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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
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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.
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56
90B C
A
60
6060C
B
A
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polygons
Classification by Sides with Flow Charts & Venn Diagrams
triangles
Scalene
Equilateral
Isosceles
Triangle
Polygon
scalene
isosceles
equilateral
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polygons
Classification by Angles with Flow Charts & Venn Diagrams
triangles
Right
Equiangular
Acute
Triangle
Polygon
right
acute
equiangular
Obtuse
obtuse
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?
Parallelogram
Two sets of parallel sides Two sets of congruent sides. The angles that are opposite
each other are congruent (equal measure).
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).
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).
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.
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.
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.
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!
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
SquareIsosceles
Trapezoid
Right
Trapezoid
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If Yes ,Join Dreams School “Campaign for Female Education”
Help us in bringing a change in a girl life, because “When someone takes away your pens you realize quite how important education is”.
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