Chapter 7.4
Special Right Triangles
Geometry
Objective(s)
A.
1. Use properties of 45­45­90 triangles.
2. Use properties of 30­60­90 triangles.
45o­45o­90o Triangles
Use the Pythagorean theorem to write the length of the hypotenuse in terms of x.
c
x
x
Rule:
Examples
1.
8
x
2.
12
x
3.
If the perimeter of a square is 24, find the length of a
diagonal.
4.
Find the values of x and y.
6
x
7
45o
.
y
Chapter 7.4
B.
Cont'd
30o­60o­90o Triangles
Start with an equilateral triangle:
When an altitude is drawn, we get
hypotenuse, c
short leg, a
long leg, b
c
b
a
2a
Rules:
1. hypotenuse: 2.
long leg: Given that each triangle is a 30o­60o­90o triangle, find the value of each variable.
Examples
1.
4
a
30o
b
2.
c
12
60o
a
Chapter 7.4
Cont'd
3.
c
a
30o
4.
Find the area of an equilateral triangle with sides 4 cm.
5.
Find the values of x, y, and z.
45o
60o
.