Geometry
Name_________________________
Unit 7 Day 4 Warmup
1. Find the unknown side length.
2. Given the side lengths of a
triangle, classify it as right, acute, or
obtuse.
26, 10, 17
x
65
72
Find the value of x.
3.
4.
x
20
x
x
5.
4
12
9
6.
20
3
2
x
25
Notes
Special Right Triangles
Today: We will understand special right triangles and how they are used.
By the end of today: You will be able to identify the angles and sides in s 30, 60, 90
triangle and a 45,45,90 triangle.
Theorem - 45°-45°-90° Triangle Theorem
45
hypotenuse = leg  2
x 2
x
45
REMEMBER THIS
General Form
x
And use in proportions
To solve for any side
Examples
Find the length of the hypotenuse.
1.
2.
8
3 2
3 2
45
Find the lengths of the legs in the triangle.
3.
5 2
4.
10
x
x
x
x
Theorem - 30°-60°-90° Triangle Theorem
hypotenuse = 2  shorter leg
60
2x
x
longer leg = shorter leg  3
30
x 3
REMEMBER THIS
General Form
And use in proportions
To solve for any side
Examples
Find the value(s) of the variable(s).
5.
6.
60
60
y
x
3
30
30
9
x
7. The logo on a recycling bin resembles an equilateral triangle with side lengths of 6 centimeters.
What is the approximate height of the logo?
8. Fill in the chart with the missing lengths.
A
30
60
C
B