Polygons

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• Polygons

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Polygons
Definition
A closed figure formed by line segments so that
each segment intersects exactly two others, but
only at their endpoints.
These figures are not polygons
These figures are 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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Classifications of a Polygon
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.
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Polygon Names
Triangle
3 sides
4 sides
Quadrilateral
5 sides
Pentagon
6 sides
Hexagon
7 sides
Heptagon
8 sides
Octagon
Nonagon
9 sides
10 sides
Decagon
Dodecagon
12 sides
n sides
n-gon
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Regular Polygons

• Regular polygons have
• All side lengths congruent
• All angles congruent

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Classifying Triangles by Sides
Scalene
A triangle in which all 3 sides are different
lengths.
AB 3.47 cm
AC 3.47 cm
AB 3.02 cm
AC 3.15 cm
Isosceles
A triangle in which at least 2 sides are equal.

• Equilateral

A triangle in which all 3 sides are equal.
GI 3.70 cm
GH 3.70 cm
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Classifying Triangles by Angles
Acute

• A triangle in which all 3 angles are less than
  90.

Obtuse
A triangle in which one and only one angle is
greater than 90 less than 180
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Classifying Triangles by Angles
Right
A triangle in which one and only one angle is 90
Equiangular
A triangle in which all 3 angles are the same
measure.
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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?

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Parallelogram

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

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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 its angle are
  right, meaning they are all 90 (four equal
  angles).

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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).

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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.

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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.

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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.

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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 its just like
  its name. When you think of right trapezoid,
  think of right angles!

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Quadrilateral Family Tree
Quadrilateral

• Its 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.

Parallelogram
Trapezoid
Rectangle
Rhombus
Isosceles Trapezoid
Right Trapezoid
Square