Special Right Triangles

1
Special Right Triangles

• 5.1 (M2)

2
Pythagorean Theorem
3
Right Triangle Theorems

• 45o-45o-90o Triangle Theorem
• Hypotenuse is times as long as each leg
• 30o-60o-90o Triangle Theorem
• Hypotenuse is twice as long as the shorter leg,
  and the longer leg is times as long as the
  shorter leg

4
EXAMPLE 1
Find the length of the hypotenuse.
a.
SOLUTION
Substitute.
5
EXAMPLE 1
Find the length of the hypotenuse.
Substitute.
Product of square roots
6
Simplify.
6
EXAMPLE 2
Find the lengths of the legs in the triangle.
SOLUTION
Substitute.
5 x
Simplify.
7
EXAMPLE 3
Standardized Test Practice
SOLUTION
8
EXAMPLE 3
Standardized Test Practice
o
o
o
45-45-90 Triangle Theorem
Substitute.
9
for Examples 1, 2, and 3
GUIDED PRACTICE
Find the value of the variable.
10
for Examples 1, 2, and 3
GUIDED PRACTICE
4. Find the leg length of a 45- 45- 90
triangle with a hypotenuse length of 6.
11
EXAMPLE 4
Find the height of an equilateral triangle
Logo
The logo on a recycling bin resembles an
equilateral triangle with side lengths of 6
centimeters. What is the approximate height of
the logo?
SOLUTION
12
EXAMPLE 5
Find the values of x and y. Write your answer in
simplest radical form.
Substitute.
Multiply fractions.
Simplify.
13
EXAMPLE 5
Substitute and simplify.
14
EXAMPLE 6
Find a height
Dump Truck
SOLUTION
15
EXAMPLE 6
Find a height
Triangle Theorem
Use a calculator to approximate.
16
EXAMPLE 6
Find a height
Substitute.
7 s
Divide each side by 2.
Substitute.
Use a calculator to approximate.
17
for Examples 4, 5, and 6
GUIDED PRACTICE
Find the value of the variable.
18
for Examples 4, 5, and 6
GUIDED PRACTICE