Geometric Relationships and Measurement

Pythagorean Theorem

Used to find the length of an unknown side in a right-angle triangle.

hyponenuse

The side opposite the right angle

is always the “c”

The other sides do not really matter which is a or b.

-to find the hypotenuse, we use the formula a^2 + b^2 = c^2
-to find the “a”, we use the formula a^2 = c^2 - b^2
-to find the “b”, we use the formula b^2 = c^2 - a^2

Perimeter and Area

composite figure

made up of more than one simple shape.

To determine the perimeter of a composite figure, ADD the distances AROUND the
outside of the figure.

To determine the area of a composite figure, ADD and/or SUBTRACT areas.

Surface Area & Volume

Volume

measure of how much space a three-dimensional object occupies

measured in cubic units.

Capacity

the maximum volume a container can hold.

measured in cubic units.

litre (L)

measure of capacity or volume often used for liquids.

prism

Volume = ( area of base ) ( height)

pyramid

Volume = ( area of base ) ( height)/3

Cone

sphere

a set of points that are all the same distance, r, from a fixed point called the centre.

Surface area

measure of how much material is required to cover or construct a three-
dimensional object.

expressed in square units.

the sum of the area of the faces.

pyramid

S.A. = A base + 4 A triangle

prism

rectangular prism

S.A. = 2 A base + 2 A sides + 2 A sides

triangular prism

S.A. = Find the surface areas of each side. Than add them together.

c^2 = a^2 + b^2

Cone

three-dimensional object with a circular base and a curved lateral surface that extends from the base to a point called the vertex.

sphere

a set of points that are all the same distance, r, from a fixed point called the centre.

MINIMIZING

For a square-based prism with a given volume, the minimum surface area occurs when the prism is a CUBE. (*Solve for the side length, s, using the Volume formula V = s^3)

For a square-based prism with a given surface area, the maximum volume occurs when the prism
is a CUBE. (* Solve for the side length, s, using the Surface Area formula SA =6s^2)

Angles

Acute

obtuse

Straight

Right

Reflex

alternate

two angles, not adjoining one another, that are formed on opposite sides of a line that intersects two other lines. If the original two lines are parallel, the alternate angles are equal.

co- interior

Interior angles form a ‘C’ pattern.

Lines

Parallel

lines that do not intersect.

transversal.

A line that intersects two or more lines, when the transversal, t, intersects lines, eight angles are formed.

called corresponding angle

Triangles

right triangle