Special Right Triangles

1
7-3

• Special Right Triangles

2
Theorem 7-8 45-45-90 Triangle Theorem

• In a 45-45-90 triangle, both legs are
  congruent and the length of the hypotenuse is v2
  times the length of a leg.

Hypotenuse (leg)(v2)
45
sv2
s
s
3
Find x
X 5v2
x
5
4
Example
In a 45-45-90 triangle the legs are congruent
Y
8
Therefore X 8
45?
The hypotenuse of a 45-45-90 triangle is (leg)(v2)
X
Therefore, Y 8 v2
5
Example
v2 leg 6
v2 x 6
v2 x 6 v2 v2
X
6
45?
x 6 v2
X
x 6 v2 v2 v2
x 6 v2 3 v2 2
6
HOMEWORK 45-45-90

• Page 369
• 1-8 all, 34,36,37
• Wksht Problems 4,5,7,9,11

7
Theorem 7-930-60-90 Triangle Theorem

• In a 30-60-90 triangle, the length of the
  hypotenuse is twice the length of the shorter
  leg. The length of the longer leg is v3 times
  the shorter leg. The shorter leg is always
  opposite the 30? angle

Hypotenuse (2)(shorter leg)
30
2s
sv3
Longer leg (v3)(shorter leg)
60
s
8
Find X and Y
Hypotenuse y Hypotenuse 2s2(5)10 Y10
30
Longer leg x Longer leg sv3 5v3 X 5v3
x
y
60
5
9
Example
2s
Hypotenuse
60?
s
5
30?
X
sv3
s 5
sv3 X 5 v3
2s Hypotenuse 10
10
Example
r (2)(7) 14
m
30?
X
m 7v3
45?
r
7
X 7
Y
Y 7v2
11
Homework 30-60-90

• Page 369
• 12-20e, 22-28e, 35,38,39
• Wksht 1,2,3,6,8,10,12,14,15,16