Geometry and Measurement: TriangleTutorial
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triangle
A geometric figure having three sides and three angles.
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Classifications
B y th e irs id es
B y th e iran g les
Trian g lesare c lass ifiedin tw o ways
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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.
No congruent sides
8cm 5cm
11cm
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Draw an isosceles triangle.
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Here is an example of an isosceles triangle.
6in 6in
4in
Two congruent sides
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Draw an equilateral triangle.
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Here is an example of an equilateral triangle.
14 ft 14 ft
14 ft
All sides congruent
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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.
70
56 54
All angles are less than 90
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º
º
º º
Draw a right triangle.
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Here is an example of a right triangle.
The “box” in the corner means 90 .
One right angle makes it a right triangle.
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º
Draw an obtuse triangle.
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Here is an example of an obtuse triangle.
100
50 30
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º
º º
Triangle Fact
The sum of the angles in a triangle must equal 180
Add the angles in these two triangles…what do you get?
100
50 30
70
56 54
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º
ºº
º
º º
Triangle Fact
70
56 54
100
50 30
100 50+ 30 180
74 56+54180
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º
º º
º
º º
Find The Missing Angle
You can find the measure of a missing angle in a triangle by taking 180º and subtracting thetwo given angles. 40º 45º
?
180-40140 140
-45 95º
OR 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 thelengths of the sides.
13m 14m
24m
13m 14m+24m 51m
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Find the perimeter of each triangle below
1.
15ft 20ft
23ft
2. 13.2in 15.4in 10.7in
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Perimeter Answers
1.
15ft 20ft
23ft
2. 13.2in 15.4in 10.7in
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
base
height
baseThe 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 = 20kmHeight = 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
13yd15yd 21yd
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Area Answer
28yd
13yd15yd 21yd
Base = 28ydHeight = 13yd
Area = (½)(28)(13)
= (14)(13)
= 182 yd2
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