Download Special Right Triangles Notes File

9.4 Special
Right Triangles
45-45-90
30-60-90
Right triangles whose
angle measures are 4545-90 or 30-60-90 are
called Special Right
Triangles.
45-45-90
30-60-90
45-45-90Theorem
In a 45-45-90 triangle, the legs are equal and the
hypotenuse equals the length of the leg times
square root of two.
If two sides of a base angles are
The same, the sides of the Angles
It share are also congruent
45
|
45-45-90
45
|
45-45-90
|
45
X
X
Legs are equal
Leg
x
2
=
hyp
X 2
45
|
Mult by 2
45-45-90
5
|
45
5
52
Legs are equal
Leg x 2 = hyp
45
|
Mult by 2
Solve for x
45
5
x 5
2
5
Going Backwards….DIVIDE
8
4 2
45
4 2
8 2 8 2
=
=
2 2 2
4 2
Div by 2
Solve for a
a
a
45
45
12
Solve for a
12  a 2
12
a
2
12 2
6 2 a
2
a
a
45
45
12
30-60-90 Theorem
In a 30-60-90 triangle, if the acute
angles are thirty degree and sixty
degree, then the side across the
hypotenuse is twice the side across
from the thirty degree angle. The
side across from the sixty degree
equals the sides across from the
thirty degree angle times square
root of three.
30-60-90 Triangles
No angles are equal so
no sides are congruent
Short
Leg
60
Hyp
30
Long Leg
30-60-90 Triangles
Short
Leg = X
60
Hyp = 2X
30
Long Leg
30-60-90 Triangles
Mult by 2
Short
Leg
60
Hyp
30
Long Leg
30-60-90 Triangles
8
60
2 x 8 = 16
30
30-60-90 Triangles
5
60
2 x 5 = 10
30
30-60-90 Triangles
Short
60
Hyp
Leg
30
Long Leg
Mult by 3
30-60-90 Triangles
15
60
Hyp
30
15 x 3 = 15 3
30-60-90
3
60
Hyp
30
3x 3 =3 3
Solve for x and r
60
r
8
30
x
Solve for x and r
60
r  16
8
30
x  8 3
Find r and x
30
r
18
60
x
Find r and x
30
r
18
60
x
18  x  3
18 18
3 18 3

*

6 3x
3
3
3
3
Find r and x
30
18
r  12 3
60
x 6 3
Going Backwards….DIVIDE
13
2
60
SL
H
LL
13
30
For now, we’ll leave it as an improper fraction
Going Backwards….DIVIDE
60
5 3
= 5 SL
3
H
LL
5 3
30
Going Backwards….DIVIDE
8 3 60
SL
3
H
LL
8
8 3
8 3
=
3 3
3
30
30-60-90 Triangles
9 3
2
30
9
2
9
5
30
10 3
3
30
12
6 3
5 3
3
6