Download Triangles

Triangles
Today’s Learning Goals
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We will learn why triangles are used in construction.
We will understand the triangle inequality – the sum
of the lengths of any two sides of a triangle is greater
than the length of the third side.
We will determine the sum of the interior angles for
any triangle.
Definitions
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A triangle is a closed, three-sided 2-D figure with
straight sides that do not overlap.
Although triangles only have three sides and three
angles, they come in many different shapes with very
useful properties.
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A right triangle is a triangle with one right angle.
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Definitions
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An acute triangle is a triangle with all angles less
than 90.
Definitions
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An obtuse triangle is a triangle with one angle more
than 90.
The terms right, acute, and obtuse are all ways that
we can name a triangle according to its angle
measurements.
Definitions
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We can also name a triangle according to its side
lengths.
A scalene triangle is a triangle where none of its
sides have the same length.
How would you name the following scalene triangles?
Scalene obtuse
Scalene right
Scalene acute
Definitions
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An isosceles triangle is a triangle that has two sides
the same length.
Often times, the same markings will be used to show
the sides with the same length.
How would you name the following isosceles triangles?
Isosceles obtuse
Isosceles acute
Isosceles right
Definitions
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What is the name of a triangle when all of its sides
are the same length?
Yes…an equilateral triangle is a triangle with
all sides the same length.
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What do you notice about the angles for all
equilateral triangles?
Excellent…they are all equal and all acute.
Triangles Are Useful
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Most of us are aware that triangles are used in the
construction of buildings, bridges, and homes.
Triangle Construction
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If you were given three different side lengths, would
you always be able to make a triangle?
Okay…some people think you would be able to and
some think you might not.
Today, we are going to try to make triangles using
metal polystrips with different side lengths.
Triangle Construction
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Let’s try to make a triangle with our metal polystrips
with lengths of 6, 8, and 10 units.
How could we name a 6, 8, 10 triangle?
Nice…it is a scalene right triangle.
8
10
Could we make a different-looking triangle
with the same three side lengths?
6
No…the 6, 8, 10 scalene right triangle is the only
one that you can make.
Notice how rigid the triangle is when we push on the
metal polystrips. This is why triangles are used in
construction…for structural stability!
Triangle Construction
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Now, let’s try to make a triangle with our metal
polystrips with lengths of 5, 9, and 16 units by
putting the 16 length on the bottom.
How come we could not make a triangle with side
lengths of 5, 9, and 16?
Yes…5 + 9 < 16 so the two sides will never meet to
make a triangle.
Triangle Construction
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Some of you thought that a triangle could be made
with any side lengths. We just saw an example of
three side lengths that did not make a triangle.
Try to make more triangles with different side lengths
greater than 3 and less than 18.
Partner Work
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You have 20 minutes to work on the following
problems with your partner.
For those that finish early
Which set of side lengths from the four below can make
a triangle with all angles the same size?
a) 5, 5, 3
b) 8, 8, 8
c) 3, 4, 5
d) 6, 8, 9
Big Idea from Today’s Lesson
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A triangle can only be made if the longest side is
shorter than the sum of the other two sides (Triangle
Inequality)!
A triangle is rigid…there’s only 1 triangle that can be
made from three given sides. This is why triangles
are used in construction.
The sum of the interior angles is 180° for ANY
triangle.
Homework
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Pgs. 225 (2 – 5, 12, 13)