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Special Cases, for Right Triangles

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Special Cases, for Right Triangles 30 60 90 Triangles 60 30 45 45 45 90 Triangles 45 * * 2 2 2 60 60 60 30 1 1 1. An equilateral triangle ... – PowerPoint PPT presentation

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Title: Special Cases, for Right Triangles


1
Special Cases, for Right Triangles 30 60 90
Triangles
60
30
45
45 45 90 Triangles
45
2
1. An equilateral triangle is also equiangular,
all angles are the same.
60
2
2. Lets draw an Altitude from one of the
vertices. Which
is also a Median and Angle bisector.
30
60
2
30
3. The bisected side is divided into two equal
segments and the bisected angle has now two 30
equal angles.
2
60
  • Congratulations! Two
  • 30 60 90 triangles have just been born
  • Oooh and you watched!!!!

3
Lets separate the top triangle and label the
unknown side as z.
apply the Pythagorean Theorem to find the unknown
side.
1
-1 -1
z
When, the smallest side is equal to 1, the
hypotenuse is 2 times as big, 1 2 2 And the
other leg is times as big, 1
Can we generalize this result for all
30-60-90 right triangles?
4
60
(2)
2
4
2
1
(2)
Yes it works!
30
(2)
Is this true for a triangle that is twice as big?
Is this true for a triangle that is half the
original size?
Yes , it still works. If we know 1 side length
of a 30-60-90 triangle, we can use this pattern
to find the other 2 sides
5
60
2
30
In a 30-60-90 triangle, the hypotenuse is
twice as long as the shorter leg, and the longer
leg is times as long as the shorter leg.
6
Find the values of the variables. Round your
answers to the nearest hundredth.
y
2x 14
30
2x 14
x
2 2
14
60
x 2
Is this 30-60-90?
90-3060
Then we know that
7
Find the values of the variables. Round your
answers to the nearest unit.
2x y
30
y
90
.
OR
60
x
x
Is this a 30-60-90?
90-6030
OR
8
Find the values of the variables. Find the exact
answer.
x
2x y
60
y
.
30
30
x
Is this a 30-60-90?
90-6030
9
Lets draw a diagonal for the square. The
diagonal bisects the right angles of the square.
What kind of right triangles are formed?
10
y
The triangles are 45-45-90
Lets draw the bottom triangle and label the
hypotenuse as y
Lets apply the Pythagorean Theorem to find the
hypotenuse.
11
45-45-90 Right Triangle
x
x
Can we generalize our findings?
12
In a 45-45-90 triangle, the hypotenuse is
times as long as a leg And both legs are the
same size.
45
s
s
45
s
13
Find the values of the variables. Round your
answers to the nearest tenth.
45
36
x
If y x
.
then
45
OR
x
y
Is this a 45-45-90?
90-4545
OR
14
Find the values of the variables. Give an exact
answer.
45
42
x
If y x
.
then
45
x
y
Is this a 45-45-90?
90-4545
15
Find the values of the variables. Give the exact
answer.
x 21
45
y
x
45
21
Is this a 45-45-90?
90-4545
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