Download 9.3 Special Right Triangles.notebook

9.3 Special Right Triangles.notebook
February 28, 2013
Geometry Agenda:
• Turn in Simplified Radical Form work
sheets for credit
• Correct 9.2 assignment
• Notes on 9.3 Special Triangles
• Quiz 9.1-9.3 Tomorrow
Mar 1­7:49 AM
Mar 1­7:48 AM
Feb 28­9:03 AM
Feb 28­9:07 AM
Lesson 9.3
Two Special Right Triangles
The Isosceles Right Triangle (45o­45o­90o triangle) is half of a square and so it shows up often in mathematics and engineering.
Let's find a shortcut for finding the length of an unknown side of an 45o ­45o ­90o triangle by applying the pythagorean theorem.
The 30o ­60o ­90o triangle is half of an equilateral triangle and can be found by folding an equilateral triangle along one of its altitudes.
Let's find a shortcut for finding the length of an unknown side of an 30o­60o­90o triangle by applying the pythagorean theorem.
8
1
1
2
5
x
14
2
5
5
x
x
45o ­45o ­90o Triangle Conjecture:
In a 45o ­45o ­90o triangle, if the legs have length x, then the hypotenuse has length x√2 .
6
x
4√2
30o ­60o ­90o Triangle Conjecture:
In a 30o ­60o ­90o triangle, if the shorter leg has length x, then the longer leg has length x√3 and the hypotenuse has length2x
x
Feb 21­5:52 AM
Feb 21­6:11 AM
1
9.3 Special Right Triangles.notebook
February 28, 2013
Lesson 9.3
Find the missing sides of these right triangles.
Two Special Right Triangles
The Isosceles Right Triangle (45o­45o­90o triangle) is half of a square and so it shows up often in mathematics and engineering.
14
p
30o
60o
f
Let's find a shortcut for finding the length of an unknown side of an 45o ­45o ­90o triangle by applying the pythagorean theorem.
6√3
t
e
1
1
5
3
4√
2
5
x
2
5
x
45 ­45 ­90 Triangle Conjecture:
In a 45o ­45o ­90o triangle, if the legs have length x, then the hypotenuse has length x√2 .
o
Find the area of this triangle
o
o
10√2
6
x
4√2
x
Feb 21­6:40 AM
Feb 21­5:52 AM
The 30o ­60o ­90o triangle is half of an equilateral triangle and can be found by folding an equilateral triangle along one of its altitudes.
Let's find a shortcut for finding the length of an unknown side of an 30o­60o­90o triangle by applying the pythagorean theorem.
Find the missing sides of these right triangles.
5
3
4√
14
5
x
14
30o ­60o ­90o Triangle Conjecture:
In a 30o ­60o ­90o triangle, if the shorter leg has length x, then the longer leg has length x√3 and the hypotenuse has length2x
Feb 21­6:11 AM
Feb 22­10:00 AM
Find the missing sides of these right triangles.
30o
f
14
6√3
p
e
60o
t
Find the area of this triangle
10√2
Feb 21­6:40 AM
2