Download 8-2: Special Right Triangles

8-2: Special Right
Triangles
G1.2.4: Prove and use the relationships among the side
lengths and the angles of 30°- 60°- 90° triangles and
45°- 45°- 90° triangles.
L1.1.6: Explain the importance of the irrational numbers
√2 and √3 in basic right triangle trigonometry, the
importance of π because of its role in circle relationships,
and the role of e in applications such as continuously
compounded interest.
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You have 1 minute to get ready for
the quiz.
Daily Quiz 5/5/2011
Determine the perimeter of the
triangle below.
32
x
3x
Isosceles Right Triangles
If a right triangle is isosceles, then it
has 2 ___________ _________
and 2 ___________ __________.
This means the measure of each
acute angle must be ______. Thus
another way to refer to Isosceles
Right Triangles is as ___________
right triangles.
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Isosceles Right Triangle
Theorem
If each leg of an isosceles right
triangle is x units long, then the
hypotenuse is xtimes the square
root of 2 units long.
45 - 45 - 90 Right
Triangles
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The triangle below is an isosceles
right triangle. What is the length of
the hypotenuse? Calculate your
answer 2 different ways.
6
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DQ 5/6/2011
An isosceles triangle has perimeter of
34.1421 feet. What is the length of
the hypotenuse of the triangle?
If one leg of an isosceles right
triangle measures 15 feet, what is
the perimeter of the triangle?
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What is the perimeter of
the square?
Class work –
2pts 2 minutes
8 2
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In an isosceles right triangle, the hypotenuse is 12.
What is the length of one (1) of the sides?
A.
6 2
B.
2 6
C.
2 4
D.
2 3
E.
3
Class work –
2pts 3 minutes
The largest triangle is equilateral
and the segment in the interior
10
is perpendicular to the base.
Determine the values of
x
x and y.
y
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30 -60 - 90 Right
Triangles
When we cut an equilateral triangle
with one altitude, we form 2
congruent right triangles each with
one 30 and one 60 degree angle.
These are called 30 - 60 - 90 right
triangles.
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30 - 60 - 90 Right
Triangle Theorem
If the shortest leg of a 30-60-90
right triangle is x units long, then
the hypotenuse is 2x units long
and the longer leg is x times the
square root of 3 units long.
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30 – 60 – 90 Triangle
30°
x√3
2x
60°
x
Solve for x and y
x
y
60
18
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Solve for x and y
x
24
60
°
y
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Solve for x and y
34.64
x
60
°
y
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An altitude of an equilateral triangle is 8.3
meters. Find the perimeter of the
triangle to the nearest tenth of a meter.
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Assignment
Pages 409 - 410,
# 11 - 21 (odds), 33
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