Geometry and Measurement: TriangleTutorial

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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

• A geometric figure having three sides and three
  angles.

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Classifications
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Classifications By Sides

• 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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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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Here is an example of an isosceles triangle.
Two congruent sides
6in
6in
4in
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Draw an equilateral triangle.
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Here is an example of an equilateral triangle.
All sides congruent
14 ft
14 ft
14 ft
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Classification by angles.

• 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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Here is an example of an acute triangle.
º
All angles are less than 90
º
º
º
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Draw a right triangle.
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Here is an example of a right triangle.
º
The box in the corner means 90 .
One right angle makes it a right triangle.
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Draw an obtuse triangle.
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Here is an example of an obtuse triangle.
º
º
º
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Triangle Fact

• The sum of the angles in a triangle must equal
  180
• Add the angles in these two triangleswhat do you
  get?

º
º
º
º
º
º
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Triangle Fact
º
100 50 30 180
º
º
º
74 56 54 180
º
º
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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.
40º 45º
40 45 85
OR
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
Awesome
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Perimeter
The perimeter of any geometric figure can be
found by adding the lengths of the sides.
13m 14m 24m 51m
13m 14m 24m
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Find the perimeter of each triangle below
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Perimeter Answers
Awesome
15ft 20ft 23ft 68ft
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 20km
Base 20km
Height 5km
Area (½)(20)(5)
(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
13yd
15yd
21yd
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Area Answer
Base 28yd
28yd
Height 13yd
Area (½)(28)(13)
13yd
(14)(13)
15yd
21yd
Awesome
182 yd2
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End Tutorial
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