Download Classifying Triangles

Objective: students will be able to understand
the basics concepts of geometry and be able to
apply them to real world problems.
 Angles
 Triangles
 Circles
 3-D
Shapes
 Area
 Volume
 Surface
Area
Let’s Get
Started!!!
Objective: to be able to examine relationships
between pairs of angles, examine relationships
of angles formed by parallel lines and a
transversal.
Model
Vertical Angles
 When
two lines
intersect, they
form two pairs of
opposite angles.
 Angles
are
congruent.
1
4
2
3
1& 2
3& 4
Symbol
1  2
Adjacent
Angles
 When
two angles
have the same
vertex between
them, share a
common side, and
do not overlap.
Model
1
4
2
3
1& 3
3& 2
Symbol
1 & 3
are adjacent angles
Complementary
Angles
 When
two angles
have the sum of 90o
Model
35o
65o
Symbol
35o + 65o = 90o
Supplementary
Angles
 When
two angles
have the sum of
180o
Model
35o
145o
Symbol
35o + 145o = 180o
Perpendicular
Lines
 When
two lines
intersect to form a
right angle.
Model
Jan is cutting a corner
off a piece of
rectangular tile.
 Classify
the
relationship
between angle x
and angle y.
 If
the m  y = 135o,
what is the measure
of  x?
The following pairs of
angles are congruent.

Alternate Interior Angles: are
on opposite sides of the
transversal and inside the
parallel lines.
 Angles 3 & 5, Angles 4 & 6

Alternate Exterior Angles: are
on opposite sides of the
transversal and outside the
parallel lines.
 Angles 1 & 7, Angles 2 & 8

Corresponding Angles: are in
same position on the parallel
lines in relation to the
transversal
 Angles 1 & 5, Angles 2 & 6,
When a transversal intersects it
forms 8 angles. Interior and
exterior angles.
Transversal Line (a line
that intersects two
parallel lines.
Parallel Line
1 2
4 3
Parallel Line
5 6
8 7
Using the figure from
page 496, answer the
following questions.
a.) Classify the
relationship between
angle 3 and angle 5.
b.) If the measure of
angle 1 is 120 degrees,
the find the measure of
angle 5 and angle 3.
Since angle 1 and angle 5 are
corresponding angles, they are
congruent and angle 5 measures
120 degrees.
Since angle 3 and angle 5
are alternate interior angles Since angle 5 and angle 3 are
congruent, angle 3 measures
they are congruent.
120 degrees also.
Using the figure in
the book, answer the
following questions.
Measure of angle
ABD = 164o
Find the measures of
angle ABC and CBD.
C
(2x + 23)o
A
Xo
D
B
Open Your Books
Way to Go!

All Triangles Have 3
Names!
First
Middle
Last
Let’s look at the first
names…
ACUTE
3 acute angles that
measure less than 90o
OBTUSE
1 obtuse angle that
measures greater than 90o
RIGHT
1 right angle that
measures 90o
Let’s look at the middle
names…
SCALENE
No equal sides
ISOSCELES
Shows that
the sides
are of equal
length
2 equal sides
EQUILATERAL
Shows that
the sides
are of equal
length
3 equal sides
Let’s look at the last
name…
TRIANGLE
Let’s look at some
examples…
What is the full name of this triangle?
Obtuse,
Scalene,
Triangle!
What is the full name of this triangle?
Acute,
Isosceles,
Triangle!
What is the full name of this triangle?
Acute,
Equilateral,
Triangle!
Looking Good, let’s
play…
Awesome
Job!
NAME THAT
TRIANGLE!!
Here are some simple rules:

Everyone will be in teams chosen by the teacher.

Everyone will have a turn at writing the answer.

Each player will write the answer of their
choosing WITHOUT the help from their
teammates. That means NO TALKING DURING
EACH ROUND.

Negative comments will result in loss of points.

Talking DURING rounds will result in loss of
points.
LET’S
PLAY!!
20
19
18
17
16
15
14
13
12
11
10
9
8
7
6
5
4
3
2
1
Acute
Equilateral
Triangle
20
19
18
17
16
15
14
13
12
11
10
9
8
7
6
5
4
3
2
1
Obtuse
Isosceles
Triangle
20
19
18
17
16
15
14
13
12
11
10
9
8
7
6
5
4
3
2
1
Obtuse
Scalene
Triangle
20
19
18
17
16
15
14
13
12
11
10
9
8
7
6
5
4
3
2
1
Right
Scalene
Triangle
GREAT JOB
EVERYONE!!!
Do we need a tie
breaker?
Let’s find the
measures of
triangles!
All triangles measure
o
180
What do they
measure?
o
180
64o
X
71o
Let’s find x.
64o
X
71o
64o + 71o = 135o
180o - 135o = 45o
x = 45o
38o
Let’s find x.
38o
X
90o + 38o = 128o
180o - 128o = 52o
x = 52o
Now, find the
measures of the
triangles!
40o
X
Let’s find x.
40o
X
X=
o
50
40o
X
25o
Let’s find x.
40o
X
X=
25o
o
115
60o
60o
X
Let’s find x.
60o
60o
X=
X
o
60
Let’s put our new
information to the test
and start our
assignment for the
day!
Circle
Time!
 Radius
 Diameter
 Central
 Chord
 Semi
Angle
Circle
What is it?
 A segment that
connects the center
point of a circle to
the circumference of
the circle
B
A
How do you name it?
 You name a radius like
a line segment starting
with the center point
first.
 Example: AB
B
A
What is it?
 A segment that
passes the center of
a circle and has both
endpoints on the
circumference of the
circle
C
A
B
How do you name it?
 You name a diameter
just like a line segment
do not name the center
C
point.
 Example: CB or BC
A
B
What is it?
 A segment that has
both endpoints on the
circumference of the
circle
C
B
How do you name it?
 You name a chord just
like you would a line
segment.
 Example: BC or CB
C
B
Objective: to be able to use the formulas for
circumference and area to solve real world
problems.
Intro to Pi Video
∏ = 3.14159…
Pi is an irrational number.
 Meaning, it goes on forever and
never repeats
 So far, mathematicians have
discovered over 134 million digits
of pi
 They’re still working to find
more…
But, all you need to know is…
∏ = 3.14

Pi is a ratio of circumference (C) to
diameter (d)
C/d = ∏
 Circumference
is the distance
 Circumference
is measured in
around a circle
units
C = (d) ∏
or
C =(2) (r) ∏
Find the circumference…
C = 10 • 3.14
10 m
C = 31.4 m
Find the circumference…
C = 2 • 2 • 3.14
2 in
C = 12.56 in
Find the circumference…
C = 2 • 8 • 3.14
C = 50.24 yd
Find the circumference…
C = 2 • 3.14
C = 6.28 cm
Great! Now
let’s move
on to area!
 Area
is the number of square
units that fit inside a circle
 Area
is measured in units2
A=∏
2
r
Can also be written…
A=∏•r•r
Find the area…
A = 3.14 • 6 • 6
6 km
A = 113.04 km2
Find the area…
A = 3.14 • 4 • 4
8 mi
A = 50.24 mi2
Find the area…
A = 3.14 • 15 • 15
A = 706.5 m2
Find the area…
A = 3.14 • 3.5 • 3.5
7 ft
A = 38.465 ft2
Super
work!!!
So how does
this apply in
the real world?

Social Studies:
◦ The circular base of the teepees of the Sioux and
Cheyenne tribes have a diameter of about 15 ft.
What is the area of the base to the nearest square
unit?
◦
◦
◦
◦
r = 15 ÷ 2
r = 7.5 ft.
A = 3.14 • 7.5 • 7.5
A = 176.625
◦ A ≈ 177 ft2

Technology:
◦ Airport Surveillance Radar (ASR) tracks planes in a
circular region around an airport. What is the area
covered by the radar if the diameter of the circular
region is 120 nautical miles?
◦ r = 120 ÷ 2
◦ r = 60 nautical miles
◦ A = 3.14 • 60 • 60
◦ A = 11304 square nautical mi

Archaeology:
◦ The large stones of Stonehenge are arranged in a
circle about 30 m in diameter. How many meters
would you have to walk if you wanted to walk the
entire distance around the structure?
◦ d = 30 m
◦ C = 30 • 3.14
◦ C = 94.2 m
Way to go!

Objective: to be able to find area of
composite figures and use that process to
solve real life problems.
Square/
Rectangle
7 ft
4 ft
L•W
28 ft2
9 cm
81 cm2
Triangle
½b•h
5 ft
4 ft
10 ft2
Circle
3.14 •
2
r
6
in
113.04 in2
9.2 m
4.3 m
7.25 m
3m
19.78 m2
21.75 m2
5 cm
19.625 m2
15 m
225 m2
Parallelogram
b•h
4 ft
5 ft
7 ft
35 ft2
Parallelogram
b•h
4 ft
6 ft
12 ft
72 ft2
Parallelogram
b•h
3.5 in
2.5 in
8 in
28.0 in2
Trapezoid
Just a reminder…name
the only characteristic
that trapezoids have.
1 set of parallel sides
Trapezoid
½ h(b1 + b2)
4 in
2 in
7 in
11 in2
Trapezoid
½ h(b1 + b2)
10 in
6 in
4 in
32 in2
Trapezoid
½ h(b1 + b2)
23 in
9 in
17 in
180 in2
Composite
Figures are made up
of two or more shapes.
To
find the area of a composite
figure, you must decompose
the figure into shapes with
areas that you know and then
find the sum of these areas!
Find the area of the
composite figure.
 The area can be
6
separated into a
m
semicircle and a
triangle.
11
m
 ½ (3.14)(r2) for circle
 ½ (b)(h) for triangle 14.1 m + 33 m = 47.1 m2
L
• W for square
20 m
20 m
13 m
Find the area of the
composite figure.
 The area can be
separated into a
trapezoid and a
rectangle.
 ½ h (b1 + b2) for
trapezoid
25 m
82.5 m + 400 m= 482.5 m2
Pedro’s father is
building a shed.
How many
square feet of
wood is needed
to build the back
of the shed
shown at the
right?
4 ft
12 ft
15 ft
210
2
ft
Find the
area of
each shape
and
subtract.

3 cm
4 cm
13 cm
7 cm
Objective: to be able to find the volume of
certain 3-D shapes to solve real world problems.
 Volume
of a three-dimensional figure is the
number of cubic units needed to fill the space
inside the figure.
A
cubic unit is a cube with edges 1 unit long
1 cm
1 cm
1 cm

To solve for volume….
area of the base • the height

Measured in cubic feet….
3
cm
length • width •
height
H
W
L

Let’s Try It
12 • 6 • 8 =
576
3
cm
Let’s Try Some
on Your Own!!
½ • base • height •
width
H
W
B

Let’s Try It
½ • 8 • 10 • 60 =
2400
3
cm
Let’s Try Some
on Your Own!!
3.14 • radius • radius •height

Let’s Try It
14
5
3.14 • 5 • 5 • 14 =
1,099
3
cm
Let’s Try Some
Word
Problems!!!
A semi has a trailer that is 32
inches long, 12 inches wide
and 22 inches high. What is
the volume of the trailer?
A tent has the shape of a
triangular prism. From the
floor to the peal is 9 feet. The
floor is 22 feet wide and 35 feet
long. What is the volume of the
tent?
A bucket has a diameter of
20 centimeters and a
height of 15 centimeters.
What is the volume?
You are sooo
good!
