Geometry
Lesson 8.2 Special Right Triangles
Name __________________________________
Let’s take a look at isosceles right triangles.
 What are the measures of the angles of any isosceles right triangle? ______, _______, _______
 Find the length of the hypotenuses of the following isosceles right triangles.

x 2  22  22
x 2  32  32
x2  8
x 2  18
x 82 2


x  18  3 2

Therefore, to find the hypotenuse of an isosceles right triangle, simple multiply a leg by ________.
Theorem 8-5: 45°-45°-90° Triangle Theorem: In a 45°-45°-90° triangle, both legs are
______________ and the length of the hypotenuses is _______ times the length of a _______.
hypotenuse 
2  leg
Thus,
leg 
hypotenuse
2
Read the following examples and then use them to help you with the practice problems.

Examples: Find the value of each variable.
hypotenuse  2  leg
h  29
h9 2
a)

hypotenuse  2  leg
x  22 2
x  2 2
x4
b)



Practice: Find the values of the variables.
1)
2)
5)
6)



leg 
c)
z

4)
7)
4 2
2
z4

3)
hypotenuse
2

Now, let’s take a look at right triangles with acute angles of measures 30° and 60°.
Theorem 8-6: 30°-60°-90° Triangle Theorem: In a 30°-60°-90° triangle, the length of the ________________
is ___________ the length of the shorter leg. The length of the ___________ leg is ______ times the
length of the shorter leg.
longer leg = 3  shorter leg
hypotenuse = 2 shorter leg
Read the following examples and then use them to help you with the practice problems.
Examples: Find the values of the variables. 
longer leg  3  shorter leg
hypotenuse  2 shorter leg
d)
8  2 x
y  3 x
4x



hypotenuse  2 shorter leg

f  2 d
longer leg  3  shorter leg
e)
5 3  3 d
5d



11)
f  2 5 10


Practice: Find the values of the variables.
8)
y4 3

9)

10)
12)
PUT IT TOGETHER!!
Practice: Find the values of the variables.
13)
14)
15)