triangles and lines – special right triangles there are two special right triangles : 30 – 60...
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Triangles and Lines – Special Right Triangles
There are two special right triangles :
30 – 60 – 90 degree right triangle
45 – 45 – 90 degree right triangle
Triangles and Lines – Special Right Triangles
There are two special right triangles :
30 – 60 – 90 degree right triangle
45 – 45 – 90 degree right triangle
30
60
In a 30 – 60 – 90 right triangle, the hypotenuse is two times longer than the shortest leg
x
2x
Triangles and Lines – Special Right Triangles
There are two special right triangles :
30 – 60 – 90 degree right triangle
45 – 45 – 90 degree right triangle
30
60
In a 30 – 60 – 90 right triangle, the hypotenuse is two times longer than the shortest leg
Using the Pythagorean theorem, we find the third side is square root of three times bigger than the shortest side.
x
2x3x
Triangles and Lines – Special Right Triangles
There are two special right triangles :
30 – 60 – 90 degree right triangle
45 – 45 – 90 degree right triangle
30
60
Example # 1 : Find the other two sides if the hypotenuse = 10
x
2x =103x
In a 30 – 60 – 90 right triangle, the hypotenuse is two times longer than the shortest leg
Using the Pythagorean theorem, we find the third side is square root of three times bigger than the shortest side.
Triangles and Lines – Special Right Triangles
There are two special right triangles :
30 – 60 – 90 degree right triangle
45 – 45 – 90 degree right triangle
30
60
Example # 1 : Find the other two sides if the hypotenuse = 10
x = 5
3x
In a 30 – 60 – 90 right triangle, the hypotenuse is two times longer than the shortest leg
Using the Pythagorean theorem, we find the third side is square root of three times bigger than the shortest side.
52
10
x
x
2x =10
Triangles and Lines – Special Right Triangles
There are two special right triangles :
30 – 60 – 90 degree right triangle
45 – 45 – 90 degree right triangle
30
60
Example # 1 : Find the other two sides if the hypotenuse = 10
x = 5
2x =103x
In a 30 – 60 – 90 right triangle, the hypotenuse is two times longer than the shortest leg
Using the Pythagorean theorem, we find the third side is square root of three times bigger than the shortest side.
52
10
x
x
35
35 is side Third
Triangles and Lines – Special Right Triangles
There are two special right triangles :
30 – 60 – 90 degree right triangle
45 – 45 – 90 degree right triangle
30
60
Example # 2 : Find the other two sides if the shortest side = 8
x = 8
2x3x
In a 30 – 60 – 90 right triangle, the hypotenuse is two times longer than the shortest leg
Using the Pythagorean theorem, we find the third side is square root of three times bigger than the shortest side.
Triangles and Lines – Special Right Triangles
There are two special right triangles :
30 – 60 – 90 degree right triangle
45 – 45 – 90 degree right triangle
30
60
Example # 2 : Find the other two sides if the shortest side = 8
x = 8
2x =163x
In a 30 – 60 – 90 right triangle, the hypotenuse is two times longer than the shortest leg
Using the Pythagorean theorem, we find the third side is square root of three times bigger than the shortest side.
16)8(2
Triangles and Lines – Special Right Triangles
There are two special right triangles :
30 – 60 – 90 degree right triangle
45 – 45 – 90 degree right triangle
30
60
Example # 2 : Find the other two sides if the shortest side = 8
x = 8
2x =163x
In a 30 – 60 – 90 right triangle, the hypotenuse is two times longer than the shortest leg
Using the Pythagorean theorem, we find the third side is square root of three times bigger than the shortest side.
16)8(2 38
Triangles and Lines – Special Right Triangles
There are two special right triangles :
30 – 60 – 90 degree right triangle
45 – 45 – 90 degree right triangle
30
60
Example # 2 : Find the other two sides if the medium length side =
x
2x
313
In a 30 – 60 – 90 right triangle, the hypotenuse is two times longer than the shortest leg
Using the Pythagorean theorem, we find the third side is square root of three times bigger than the shortest side.
3133x
Triangles and Lines – Special Right Triangles
There are two special right triangles :
30 – 60 – 90 degree right triangle
45 – 45 – 90 degree right triangle
30
60
Example # 2 : Find the other two sides if the medium length side =
x = 13
2x
313
In a 30 – 60 – 90 right triangle, the hypotenuse is two times longer than the shortest leg
Using the Pythagorean theorem, we find the third side is square root of three times bigger than the shortest side.
3133x
Triangles and Lines – Special Right Triangles
There are two special right triangles :
30 – 60 – 90 degree right triangle
45 – 45 – 90 degree right triangle
30
60
Example # 2 : Find the other two sides if the medium length side =
x = 13
2x = 26
313
In a 30 – 60 – 90 right triangle, the hypotenuse is two times longer than the shortest leg
Using the Pythagorean theorem, we find the third side is square root of three times bigger than the shortest side.
3133x
26)13(2
Triangles and Lines – Special Right Triangles
There are two special right triangles :
30 – 60 – 90 degree right triangle
45 – 45 – 90 degree right triangle
45
45
Remember, sides opposite equal angles are congruent. If we let AC and BC = 1 and use Pythagorean theorem…
1
1
A
C B
?
Triangles and Lines – Special Right Triangles
There are two special right triangles :
30 – 60 – 90 degree right triangle
45 – 45 – 90 degree right triangle
45
45
Remember, sides opposite equal angles are congruent. If we let AC and BC = 1 and use Pythagorean theorem…
1
1
A
C B
2
2
112
222
c
c
c
2
Triangles and Lines – Special Right Triangles
There are two special right triangles :
30 – 60 – 90 degree right triangle
45 – 45 – 90 degree right triangle
45
45
The hypotenuse of a 45 – 45 – 90 right triangle is square root two times larger than the equal sides…
x
x
A
C B
2x
Triangles and Lines – Special Right Triangles
There are two special right triangles :
30 – 60 – 90 degree right triangle
45 – 45 – 90 degree right triangle
45
45
The hypotenuse of a 45 – 45 – 90 right triangle is square root two times larger than the equal sides…
6
6
A
C B
2x
Example # 1 : Find the hypotenuse if the congruent sides = 6
Triangles and Lines – Special Right Triangles
There are two special right triangles :
30 – 60 – 90 degree right triangle
45 – 45 – 90 degree right triangle
45
45
The hypotenuse of a 45 – 45 – 90 right triangle is square root two times larger than the equal sides…
6
6
A
C B
26
Example # 1 : Find the hypotenuse if the congruent sides = 6
Triangles and Lines – Special Right Triangles
There are two special right triangles :
30 – 60 – 90 degree right triangle
45 – 45 – 90 degree right triangle
45
45
The hypotenuse of a 45 – 45 – 90 right triangle is square root two times larger than the equal sides…
x
x
A
C B
215
Example # 2 : Find the congruent sides if the hypotenuse = 215
Triangles and Lines – Special Right Triangles
There are two special right triangles :
30 – 60 – 90 degree right triangle
45 – 45 – 90 degree right triangle
45
45
The hypotenuse of a 45 – 45 – 90 right triangle is square root two times larger than the equal sides…
15
15
A
C B
215
Example # 2 : Find the congruent sides if the hypotenuse = 215