Download Geometry Review

Math 9 Numeracy – Unit 7.7
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Geometry Review
7.7 – Geometry Review
During the course of this unit we have examined the basic geometric shapes, angles,
triangles, perimeters and areas of both rectangles and circles. You have also examined how
to interpret and create circle graphs. This review package will go over all of these concepts
and will provide you with some practice questions in order to prepare you for your unit exam.
Here are the basic geometric shapes you will have to know;
You will also need to know these lines.
Identifying Angles
An angle is made up of two rays that meet at a point know as a vertex.
Point A is the vertex of angle BAC. Line AB and Line AC meet at Point A. Lines are
identified by two points, as in Line AB. Angles are identified by three points with the
middle point always being the vertex as in Angle BAC.
An angle is measured in terms of a unit knows as a “degree” ( o). There are 360 o in a circle.
Here are some common angles;
Triangles
A triangle consists of three connecting line segments enclosing three angles. Each triangle
can be classified by the type of angles that it contains;
or by their sides;
Measuring the Angles in a Triangle
You MUST remember that if you were to add up all the angles within a triangle the sum
would equal 1800. That means that if you knew what two of the angles were, you could
always solve for the third by subtracting the other two from 180.
Perimeter
The perimeter of a shape is simply the total distance AROUND the shape. To calculate the
perimeter, simply measure the sides, and add up those measurements. Examine the
following examples;
Area
The space within a shape is called area. The area of a square and a rectangle use the
formula; Area = base x height or A = b x h
For example;
Finding the Area of a Parallelogram
Finding the area of a parallelogram is a bit trickier only because the sides of a parallelogram
are usually at a slant. In order to find the height that can then be used in your formula
A = B x H, you have to find the height as it relates to a right angle. Almost all questions
that you come across that ask you to calculate the area of a parallelogram; will somehow
make that right-angle height known to you. You may have to look for it, but it will be there.
*Note* When
calculating the area of
a parallelogram your
height is always found
by the right-angle
measurement. NOT
the length of the
slanted side!
Finding the Area of a Triangle
To calculate the area of a triangle, you have to use a different formula. That is because a
triangle is essentially one half of a rectangle.
Because a triangle is half of a rectangle you simple take the formula for a rectangle
( A = B x H ) and divide it by 2.
Circumference
Like perimeter, the circumference of a circle is the
distance AROUND the outside. Unlike an object with
straight side, the circumference of a circle is more
difficult to calculate, in fact, you need a formula to solve
the circumference of a circle.
In order to use the formula for the circumference of a
circle, you have to know two terms as they relate to a
circle; the diameter and the radius. The diameter is the
straight line, from one side of the circle through the next, straight through the middle.
The radius is a straight line, staring from the middle and extending out to a side.
In order to solve the problem of calculating the circumference of a circle we have to use a
very specific ratio which in this case is called pi and is represented by the Greek symbol;
Pi has a value of 3.14
Because the radius is half the size of the diameter, the formula for the circumference (c)
can either be expressed using radius (r) or diameter (d);
Area of a Circle
The area of a circle is simply the amount of space contained within a circle. Like all other
area questions, answers are ALWAYS in “units squared” such as cm2 or in.2. Study the
example questions provided below;
Interpreting Circle Graphs
A circle graph is sometimes called a pie graph. It shows how a total amount has been
divided into parts according to percents. The percents of a circle graph always add up to
100%.
The following circle graph shows the inventory at Future Shop, an electronics superstore.
Calculating Amounts from Circle Graph Percents
Because circle graphs are expressed as percents of an amount, the specific amount can be
calculated by multiplying the decimal form of the percent (always use the decimal form of a
percent when you use calculations) by the total amount the pie graph is representing. For
example;
What is the new inventory dollar amount that Future Shop has in computer stock?
Solution:
Circle Graphs
Pie graphs are another way of representing information in a graphical, but easy to
understand manner. Pie graphs convert percentages into degrees and then map out “pieces
of pie” in a circle. For example, if you had a data table that had collected information on
what a group of 200 people thought were Mr. Trickey’s best attributes, it may look
something like this;
Mr. Trickey’s Attributes
His athletic prowess
36
His sense of humour
18
His rugged good looks
54
His keen fashion sense
10
His ability to attract “the ladies”
82
Total People Interviewed
200
In order to convert this data into a pie graph we must first convert the data into a
percentage and then multiply that percentage by 360. We multiply by 360 because there
are 360 degrees in a complete circle. Once we have converted our data into degrees we can
then use a protractor to draw our pie graph.
Mr. Trickey’s Attributes
Data
Convert to %
His athletic prowess
36
36/200 = 18%
His sense of humour
18
18/200 = 9%
His rugged good looks
54 54/200 = 27%
His keen sense of fashion
10
10/200 = 5%
His ability to attract “the ladies”
82
72/200 = 41%
Totals
200
100%
Convert to Degrees
0.18 x 360 = 65 degrees
0.09 x 360 = 32 degrees
0.27 x 360 = 97 degrees
0.05 x 360 = 18 degrees
0.41 x 360 = 148 degrees
360 Degrees
We can then use a protractor to map out and then label our pie graph to look like this;
Fashion Sense
Athletic Prowess
Humour
Good Looks
Ability to attract
“the ladies”
Math 7 – Unit 7.7
Geometry Review
7.7 – Geometry Review - Practice Questions
Directions: Name the following shapes;
_______________
________________
_______________
Directions: Name the following angles;
_______________
Directions: Find the following angles;
Angle A = _______
Angle B = _______
Angle C = _______
________________
_______________
Angle X = _______
Angle Y = _______
Angle Z = _______
Directions: Name the following type of triangle;
___________________
___________________
_________________
___________________
_________________
Directions: Find the missing angles
__________________
Directions: Find the perimeter of the following shapes; Show all your work for full marks!
Directions: Calculate the following areas. Start with the formula and then show all your
work for full marks!
Directions: Use the information provided to complete the data table and then use a
protractor to create an accurate circle graph.
Favourite Type of Ice Cream
Data
Convert to a %
Convert to Degrees
Activity
Chocolate
125
Vanillia
160
Strawberry
75
Tiger
50
Bubble Gum
90
Total
100%
3600
Title of graph:
Title of graph:
Cut out the protractor provided
and starting at 0 degrees measure
out your “pie pieces” according to
your calculations above