Download Plane Shapes

Polygons
A polygon is a plane shape with straight sides.
Is it a Polygon?
• Polygons are 2-dimensional shapes. They are
made of straight lines, and the shape is
"closed" (all the lines connect up).
Polygon
(straight sides)
Not a Polygon
(has a curve)
Plane Shapes
Not a Polygon
(open, not closed)
2
Types of Polygons:
Simple or Complex
A simple polygon has only one boundary, and it doesn't cross
over itself. A complex polygon intersects itself!
Simple Polygon
Complex Polygon
(this one's a Pentagon)
(also a Pentagon)
Plane Shapes
3
Types of Polygons:
Concave or Convex
•
•
A convex polygon has no angles pointing inwards. More
precisely, no internal angles can be more than 180°.
If there are any internal angles greater than 180° then it is
concave. (Think: concave has a "cave" in it)
convex
concave
Plane Shapes
4
Types of Polygons:
Regular or Irregular
If all angles are equal and all sides are equal, then it is
regular, otherwise it is irregular
regular
irregular
Plane Shapes
5
More Examples
Complex Polygon
Concave Octagon
Irregular Hexagon
(a "star polygon",
in this case, a
pentagram)
Plane Shapes
6
Names of Polygons
If it is a Regular Polygon..
Interior Angle
Shape
Name
Sides
Triangle (or Trigon)
3
60°
Quadrilateral (or Tetragon)
4
90°
Pentagon
5
108°
Hexagon
6
120°
Heptagon (or Septagon)
7
128.571°
Octagon
8
135°
Nonagon (or Enneagon)
9
140°
Decagon
10
144°
Dodecagon
12
150°
Plane Shapes
7
Regular 2-D Shapes - Polygons
Triangle
Square
Pentagon
Hexagon
Heptagon
Octagon
Nonagon
Decagon
Hendecagon
Dodecagon
These shapes are known as regular polygons. A polygon is a many sided shape
with straight sides.
Plane Shapes
To be a regular polygon all the sides and angles must be the same.
8
Triangles
Equilateral Triangle
Three equal sides
Three equal angles, always 60°
Isosceles Triangle
Two equal sides
Two equal angles
Scalene Triangle
No equal sides
No equal angles
Plane Shapes
9
Triangles
Acute Triangle
All angles are less than 90°
Right Triangle
Has a right angle (90°)
Obtuse Triangle
Has an angle more than 90°
Plane Shapes
10
Combining the Names
Sometimes a triangle will have two names, for example:
Right Isosceles Triangle
Has a right angle (90°), and also two equal angles
Can you guess what the equal angles are?
Plane Shapes
11
Quadrilateral
Quadrilateral just means "four sides"
(quad means four, lateral means side).
Any four-sided shape is a Quadrilateral.
But the sides have to be straight, and it has to be 2-dimensional.
Plane Shapes
12
Properties
Four sides (or edges)
Four vertices (or corners).
The interior angles add to 360
degrees.
Try drawing a quadrilateral, and measure the
angles. They should add to 360°.
Plane Shapes
13
Types of Quadrilaterals
There are special types of quadrilateral:
If it isn't one of those it is an irregular
quadrilateral.
Some types are also included in the
definition of other types! For example a
square, rhombus and rectangle are
also parallelograms.
Plane Shapes
14
The Rectangle
A rectangle is a four-sided shape where every
angle is a right angle (90°).
Also opposite sides are parallel and of equal
length.
Plane Shapes
15
The Rhombus
A rhombus is a four-sided shape where all sides
have equal length.
Also opposite sides are parallel and opposite
angles are equal.
Another interesting thing is that the diagonals
(dashed lines in second figure) of a rhombus
bisect each other at right angles.
Plane Shapes
16
The Square
A square has equal sides and every angle is a right
angle (90°).
Also opposite sides are parallel.
A square also fits the definition of a rectangle (all
angles are 90°), and a rhombus (all sides are
equal length).
Plane Shapes
17
Parallelogram
Opposite sides are parallel and equal in length,
and opposite angles are equal (angles "a" are the
same, and angles "b" are the same)
NOTE: Squares, Rectangles and Rhombuses
are all Parallelograms!
Example: if a parallelogram has all sides equal
and angles "a" and "b" are right angles, then it is
also a square.
Plane Shapes
18
Trapezium
Trapezium
Isosceles Trapezium
(US: Trapezoid)
A trapezium (called a trapezoid in the US) has one
pair of opposite sides parallel.
It is called an Isosceles trapezoid if the sides that
aren't parallel are equal in length and both angles
coming from a parallel side are equal, as shown.
A trapezoid is not a parallelogram because only
one pair of sides is parallel.
Language Note: In the US a "trapezium" is a quadrilateral with NO
parallel sides!
Plane Shapes
19
The Kite
Hey, it looks like a kite. It has two pairs of sides.
Each pair is made up of adjacent sides that are
equal in length. The angles are equal where the
pairs meet. Diagonals (dashed lines) meet at a
right angle, and one of the diagonal bisects (cuts
equally in half) the other.
Plane Shapes
20
Irregular Quadrilaterals
Any quadrilateral that doesn't match one of the
previous types.
Plane Shapes
21
22
The "Family Tree" Chart
Plane Shapes
References / Sources:
http://www.mathsisfun.com/geometry/polygons.html
Plane Shapes
23