Download Geometry Guided Notes – Lesson 8.2 Special Right Triangles Name __________________________________

Geometry
Guided Notes – 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

* Copy theorem 8-5 onto your tan theorem
sheet *
Examples: Find the value of each variable.
hypotenuse  2  leg
h  29
h9 2
a)



Practice: Find 
the values of the variables.
1)
hypotenuse  2  leg
x  22 2
x  2 2
x4
b)
2)



3)
leg 
c)
z

4 2
2
z4

4)
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
* Copy theorem 8-6 onto your tan theorem sheet *
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



Homework: p.428 #1-5, 6, 8-14, 17, 18, 21
f  2 5 10


Practice: Find the values of the variables.
5)
y4 3

6)

7)
THT: Do problems #6-9