Transcript Special Right Triangles

Special Right Triangles
Lesson 8.4
Geometry Honors
Lesson Focus
There are two types of right triangles that occur very
frequently in solving problems. This lesson studies these two
types of triangles, which are named by the size of their
angles: the 45-45-90 triangle and the 30-60-90triangle.
45- 45- 90 Triangle
In a 45- 45- 90 triangle, the hypotenuse is 2 times as long
as the leg.
A
45
x 2
x
45
C
x
B
45- 45- 90 Triangle
Example 1: Find the value of x.
A
6
x
45
C
x
B
30- 60- 90 Triangle
In a 30- 60- 90 triangle, the hypotenuse is twice as long as
the shorter leg, and the longer leg is 3 times as long as the
shorter leg.
A
60
x
2x
30
C
x 3
B
30- 60- 90 Triangle
Example 2: Find the value of x and y.
A
y
5
30
C
x
B
Special Right Triangles
45-45-90 triangle
Hyp.  2  S.L.
Hyp.  2  Leg
Hyp.
Leg 
2
S .L. 
Hyp.
2
L.L.
S .L. 
3
L.L.  3   S.L.
A
A
x 2
x
C
30-60-90 triangle
x
2x
x
B
C
x 3
B
Special Right Triangles
Given:
S
t
r
45
T
s
R
1. If r = 6, t = ____
2. If s = 2, t = ____
3. If t = 2 , r = ____
4. If t = 10, s = ____
Special Right Triangles
Given:
P
n
q
30
N
p
Q
1. If q = 8, p = ____ and n = ____.
2. If n = 20, q = ____ and p = ____.
3. If p = 4 3, q = ____ and n = ____.
4. If p = 9, q = ____ and n = ____.
Special Right Triangles
A diagonal of a square has length 6. What is the perimeter of
the square?
Written Exercises
Problem Set 8.4A, p.302: # 2 - 32 (even), 38