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FINDING PERIMETER
1.
Perimeter is defined as the sum of the
lengths of the sides of a polygon.
2.
Perimeter is really just adding up of all the
sides of a polygon.
8
8
6
10
6
8
7
Perimeter = 6 + 8 + 6 + 8
Perimeter = 8 + 7 + 10
Perimeter = 28
Perimeter = 25
FINDING AREA
1. Area is defined as the number of square units that covers
a shape or figure.
2. Area is really just how much space is inside a polygon.
Square or Rectangle
Area = Length x Width
Triangle
Area = (base x height) / 2
W
h
L
b
6
8
8
7
Area = 8 x 6
Area = 48
Area = (7 x 8)/2
Area = 28
Note: For triangles, the height must be perpendicular to the base.
Finding Area (Cont.)
Parallelogram
Area = base x height
Circle
Area = π x radius2
r
h
b
5
4
6
Area = 4 x 6
Area = 24
Area = (3.14) x 5
Area = 15.7
Note: For parallelograms, the height must be perpendicular to the base.
Edges
1. The line segment where two faces of a solid
figure meet.
2. The line where two sides meet on a 3-D
shape.
Faces
1. A flat surface of a three-dimensional figure.
2. The side of a 3-D figure.
This cube has
6 faces.
This square
based pyramid
has 5 faces.
FINDING VOLUME
1. Volume is defined as the measure of space, or capacity.
2. Volume is really just how much space is inside a 3-D
figure.
H
W
L
Volume = Height x Width x Length
5
5
5
Volume = 5 x 5 x 5 = 125
Pairs of Lines
Parallel
Two lines are parallel if they never intersect.
Intersecting
Lines that cross at only one point.
Perpendicular
Lines that intersect at a right angle (90 degrees).
Geometry Terms
A location in a plane or in
space, having no
dimensions.
Z
Point
B
A
Ray
A part of a line, with one
endpoint, and extending to
infinity in one direction.
AB
A straight set of points that
extends into infinity in both
directions.
D
C
Line
CD
E
Two points on a line, and
all the points between those
two points.
F
Line Segment
EF
The union of two rays with
a common endpoint, called
the vertex.
G
Angle
H
GHI∠
I
A flat surface that stretches
into infinity.
Plane
Types of angles
Acute
A positive angle measuring less
than 90 degrees.
Right
An angle whose measure is 90
degrees.
Obtuse
An angle whose measure is
greater than 90 degrees.
Straight
An angle whose measure is 90
degrees.
Types of Triangles
Side Names
Equilateral
A triangle that has three
equal sides.
Isosceles
A triangle with at least two
equal sides.
Scalene
A triangle with three
unequal sides.
Angle Names
Acute
A triangle with all three
angles that measure less
than 90 degrees.
Right
A triangle with only one
right angle.
Obtuse
A triangle with only one
obtuse angle.
Types of Special Quadrilaterals
Name
Shape
Characteristics
-
Four equal sides
Four equal angles
2 sets of parallel sides
-
Four equal angles
2 sets of parallel sides
-
Four equal sides
2 sets of parallel sides
Square
Rectangle
Rhombus
Note: Opposite angles are
equal.
-
Parallelogram
Note: Opposite angles are
equal.
-
Trapezoid
2 sets of parallel sides
Only 1 set of parallel sides
Types of 3-D Shapes
Name
Shape
Characteristics
A three-dimensional figure
with six square faces.
Cube
Rectangular Prism
Cylinder
Cone
Pyramid
Sphere
A three-dimensional figure
with a six faces, two of
which must be rectangles.
A three-dimensional figure
having two parallel bases
that are congruent circles.
A three-dimensional figure
with all points in space a
fixed distance from a given
point, called the center.
A three-dimensional figure
that has a polygon for its
base and whose faces are
triangles having a common
vertex.
A three-dimensional figure
with one vertex and a
circular base.
Polygons
Polygon – A 2 dimensional closed figure made up of at least 3
sides that are straight.
Polygons
Not Polygons
Regular Polygon – A polygon in which all the angles are equal and
all of the sides are equal.
Regular Polygons
Non-regular Polygons
Types of Polygons
Name
Number of
Sides
Number of
vertices
Number of
angles
Sum of
Angles
Triangle
3
3
3
180°
Quadrilateral
4
4
4
360°
Pentagon
5
5
5
540°
Hexagon
6
6
6
720°
Heptagon
7
7
7
900°
Octagon
8
8
8
1080°
Nonagon
9
9
9
1260°
Decagon
10
10
10
1440°
Circles
chord
diameter
radius
Term
diameter
radius
chord
Term
Definition
Symbol
The line segment joining two points on a
circle and passing through the center of the
circle.
The distance from the center to a point on a
circle; the line segment from the center to a
point on a circle.
A line segment that connects two points on a
curve.
Definition
π
r
No symbol
Formula
Circumference The distance around a circle.
Area of a
The number of square units
Circle
that covers a circle.
**Note:
d
= 3.14
π ×d
or
2×π ×r
π × r2
Congruent Polygons
Two polygons are congruent if they are the same size and shape – that is, the
corresponding angles of the two polygons are the exact same size, and the corresponding
sides of the two polygons are the exact same size.
For two polygons to be congruent, the figures do not need to be in the same position.
Congruent
Not Congruent
Similar Polygons
Two polygons are similar if they are the exact same shape but not the same size –
that is, the corresponding angles of the two polygons are the exact same size, but the
corresponding sides of the two polygons are different sizes (but proportional).
For two polygons to be similar, the figures do not need to be in the same position.
Similar
Not Similar