Geometry and
Measurement:
TriangleTutorial
Before you begin you will
want to have paper and
pencil for notes and a
straight edge (ruler).
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triangle

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A geometric figure having three
sides and three angles.
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Classifications
Trian g les
are classified
in two ways
B y th eir
sid es
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B y th eir
an g les
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Classifications By Sides
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Scalene-all sides are of different
lengths (no congruent sides)
Isosceles-two sides are the
same length (two sides
congruent)
Equilateral-all sides the same
length (all sides congruent)
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Draw a scalene triangle.
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you are done drawing
Here is an example of a
scalene triangle.
8cm
5cm
11cm
No congruent sides
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Draw an isosceles
triangle.
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you are done drawing
Here is an example of
an isosceles triangle.
6in
6in
4in
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Two
congruent
sides
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Draw an equilateral
triangle.
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you are done drawing
Here is an example of
an equilateral triangle.
All sides
congruent
14 ft
14 ft
14 ft
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Classification by angles.
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Acute - a triangle having all
angles acute (smaller than 90º)
Right - a triangle with one right
angle (90º)
Obtuse - a triangle with one
obtuse angle (greater than 90º
and smaller than180º)
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Draw an acute triangle.
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are done drawing
Here is an example of
an acute triangle.
All angles are
less than 90 º
70 º
56 º
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54º
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Draw a right triangle.
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you are done drawing
Here is an example of a
right triangle.
The “box” in the corner means 90º.
One right angle makes
it a right triangle.
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Draw an obtuse triangle.
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you are done drawing
Here is an example of
an obtuse triangle.
100 º
50 º
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30º
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Triangle Fact
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The sum of the
100º
angles in a
triangle must
50º
equal 180
Add the angles
70º
in these two
triangles…what
do you get?
56º
30º
54º
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Triangle Fact
100º
30º
50º
70º
56 º
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54º
100
50
+ 30
180
74
56
+54
180
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Find The Missing Angle
You can find the measure of a
missing angle in a triangle by
taking 180º and subtracting the
two given angles.
180
-40
140
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140
-45
95º
OR
?
40º
45º
40
+45
85
180
- 85
95º
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Find The Missing Angle
1. Two angles in a triangle are 35º and
65º. Find the third side.
2. Two angles in a triangle are 15º and
100º. Find the third side.
3. Two angles in a triangle are 60º and
60º. Find the third side.
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Missing Angle Answers
1. 180 - 65 - 35 = 80º
2. 180 - 15 - 100 = 65º
3. 180 - 60 - 60 = 60º
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Perimeter
The perimeter of any geometric
figure can be found by adding the
lengths of the sides.
13m
14m
13m
14m
+24m
51m
24m
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Find the perimeter of
each triangle below
2.
1.
15ft
20ft
13.2in
15.4in
10.7in
23ft
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Perimeter Answers
1.
2.
15ft
20ft
13.2in
15.4in
10.7in
23ft
15ft + 20ft + 23ft
= 68ft
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13.2in + 15.4in + 10.7in
= 39.3in
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Area
Finding the area of a triangle can be a
little tricky. You must know two
pieces of information. You must know
the height of the triangle and you
must know the length of the base.
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Base and Height
height
height
base
base
The height and base ALWAYS meet at a
right angle.
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Area Formula
The formula for the area
of a triangle is
½ base X height.
This is the same as
base X height ÷ 2
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Area Example
6km
12km
5km
Base = 20km
Height = 5km
Area = (½)(20)(5)
20km
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= (10)(5)
= 50 km2
Remember, all area answers must
have an exponent of 2 on the label.
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Find the area of the
triangle below.
28yd
15yd
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13yd
21yd
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Area Answer
28yd
15yd
Base = 28yd
Height = 13yd
Area = (½)(28)(13)
13yd
21yd
= (14)(13)
= 182
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yd2
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