Download Geometry Notes from Mr. Martin

Types of quadrilaterals
rhombus
Geometry Notes
NAME of Shape
triangle
quadrilateral
pentagon
hexagon
heptagon
octagon
decagon
# of sides
3 sides
4 sides
5 sides
6 sides
7 sides
8 sides
10 sides
Type of Triangle
Equilateral
Isosceles
Scalene
Right Triangle
Has 2 sets of parallel lines
and all lines are of equal
length.
Has one set of parallel lines
and 2 lines are of equal
length.
Has 2 sets of parallel lines
Has 2 sets of parallel lines
and all 4 sides are equal.
Has 2 sets of parallel lines
and 2 sets of equal length
lines.
trapezoid
Paralleogram
square
rectangle
Description
All 3 sides are of equal length
2 sides of equal length
no sides equal length
has a right angle
Name of Angle
Acute angle
Obtuse angle
Right angle
Straight angle
Complimentary angles
Supplementary angles
Description
Less than 90°
Greater than 90°and less than 180°
Equal to 90°
Equal to 180°
2 angles that equal 90°
2 angles that equal 180°
This is a compass. It is used to draw circles.
d
Diameter: A line which
passes through the center,
from side to side.
Radius: A line from the center
to a point on the circumference
r
π is the symbol “pi”
We will use the number 3.14 for π
Circle Formulas

Cicumference: the line
around the outside of a
circle. It is the perimeter of
the circle.
The radius is always ½ of the diameter. This means that the diameter is always 2x (twice)
the radius.
Circumference of a circle =
of the circumference.
Area of a circle =
πr²
πd
This means you multiply 3.14 x the length of the diameter to find the length
This means you multiply 3.14 x the radius x the radius
Rectangles: Are quadrilaterals and parallelograms. They have 2 sets of parallel lines and four 90º angles.
To find the perimeter of a rectangle, simply add up all four sides. Remember to add up 4 sides. If I label only 2
sides, you must figure out the length of the unlabelled sides. This is easy because the 2 long sides are equal and
the 2 shorts sides are equal.
Find the perimeter of this rectangle: The perimeter of this rectangle will be 12+12+5+5= 34 cm.
Perimeter: Just add up all the sides.
Length 12 cm
Width
5 cm
Area: Length x width
Now find the area.
The formula for the area of a rectangle is A= l x w (length x width)
So 12 cm x 5 cm = 60 cm²
The area is 60 cm²
Finding the missing angle:
To find the missing angle in any triangle or quadrilateral you need to remember this:
All the angles in a triangle add up to 180º and all the angles in any quadrilateral add up to 360º
Since all the angles of a triangle must equal
180º, I know that 60º + 40º + X = 180º.
60º
40º
180º
X must be 80º , because 60º+40º+80º=180º
Xº
Try another: Find the missing angle in this quadrilateral.
110º
80º
80º
Xº
WJM VIII
Mr. Martin said that all the angles in any
quadrilateral must equal 360º, so that
means 110º + 80º + 80º + Xº = 360º.
X must be 90º, because
110º + 80º + 80º + 90º = 360º
Triangles
Side 15cm
A= ½bh
This is a right triangle because it has a right (90°) angle.
height
10cm
Triangle formula: To find the area of a triangle:
A= ½bh means you multiply ½ of the base x the height.
Example: Find the area of this triangle.
base 6cm
In this case ½ of the base = 3cm (½ of 6 is 3) and the height is
10 cm. So 3 x 10 = 30 cm² The area of this triangle is 30 cm
The height must be a line perpendicular (can’t be slanted or diagonal) to the base.
Height
10cm
Side 12cm
The area of this triangle (A= ½bh ) will be 6 X 10=60cm²
The base is 12cm, so half of 12cm is 6cm. The height is
10cm so 6 X 10 = 60
Side
12cm
Base
12cm
Two triangles make a quadrilateral:
Height or
width
base or length
The area of a rectangle is A= l x w which is the same as saying A= b X h. A triangle is half of this. or
A = b x h Why is a triangle ½ of the rectangle? Look at the two triangles making a rectangle. Notice how
they make half of a rectangle? That’s why the formula for a triangle is ½ b x h because a triangle is half the
rectangle.
Geometry of Cubes.
Cubes have: 6 faces (sides)
8 vertices (corners) Vertices is the plural of vertex
12 edges. (edges)
This is a pattern (aka jacket) which can be folded into a cube.
It is made of six congruent squares. (I tried anyways)
It is a solid figure, or a 3D shape.
Face
Edge
Vertex
FORMULAS
 To calculate the area of each face simply multiply the length by the width. A = l x w
 To calculate the surface area of a cube: find the area of one face and then multiply by 6.

To calculate the volume of a cube multiply length by width by height V=l
xwxh
Length
width
WJM VIII
Formulas:
Remember that two letters beside each other means Multiply them together.
l= length; w = width; b = base; h = height; r = radius; c=circumference
Area of a Rectangle
A=lw
Area of a Parallelogram
A= bh
Area of a Triangle
A = ½bh
Area of a Circle
A = r2 (=3.14)
Circumference of a Circle
C = 2r
Volume of a Cube
V = lwh
Volume of a Sphere
V = (4/3)r3
Volume of a Cone
V = (1/3)r2h
Volume of a Cylinder
V = r2h
Surface Area of a Sphere
A = 4r2