1. Tuesday, February 2
Essential Questions
How do I use the relationships among the sides in special right triangles?

2. Special Right Triangles
5.1
Special Right Triangles
Theorem 5.1: 45o – 45o – 90o Triangle Theorem
In a 45o – 45o – 90o triangle, the hypotenuse is ____ times as long as each leg.

3. Special Right Triangles
5.1
Special Right Triangles
Example 1
Find lengths in a 45o – 45o – 90o triangle
Find the value of x.
Solution
By the Triangle Sum Theorem, the measure of the third angle must be ______. Then the triangle is a ____-____- 90o triangle, so by Theorem 5.1, the hypotenuse is ___ times as long as each leg.
____-____- 90o Triangle Theorem
Substitute.

4. Special Right Triangles
5.1
Special Right Triangles
Example 1
Find lengths in a 45o – 45o – 90o triangle
Find the value of x.
Solution
You know that each of the two congruent angles in the triangle has a measure of ____ because the sum of the angle measure in a triangle is 180o.
____-____- 90o Triangle Theorem
Substitute.
Divide each side by ___.
Simplify.

5. Special Right Triangles
5.1
Special Right Triangles
Checkpoint. Find the value of x.

6. Special Right Triangles
5.1
Special Right Triangles
Checkpoint. Find the value of x.

7. Special Right Triangles
5.1
Special Right Triangles
Theorem 5.2: 30o – 60o – 90o Triangle Theorem
In a 30o – 60o – 90o triangle, the hypotenuse is ____ as long as the shorter leg, and the longer leg is ____ times as long as the shorter leg.

8. Special Right Triangles
5.1
Special Right Triangles
Example 2
Find the height of an equilateral triangle
Music You make a guitar pick that resembles an equilateral triangle with side lengths of 32 millimeters. What is the approximate height of the pick?
Solution
Draw the equilateral triangle described. A B C
Its altitude forms the longer leg of two ___-___- 90 triangles. The length h of the altitude is approximately the height of the pick.

9. Special Right Triangles
5.1
Special Right Triangles
Example 3
Find lengths in a 30o – 60o – 90o triangle
Find the values of x and y. Write your answer in simplest radical form.
Solution
Step 1
Find the value of x.
Substitute.
Divide each side by ___.
Multiply numerator and denominator by ___.
Multiply fractions.

10. Special Right Triangles
5.1
Special Right Triangles
Example 3
Find lengths in a 30o – 60o – 90o triangle
Find the values of x and y. Write your answer in simplest radical form.
Solution
Step 2
Find the value of y.

11. Special Right Triangles
5.1
Special Right Triangles
Checkpoint. Find the value of the variable.

12. Special Right Triangles
5.1
Special Right Triangles
Checkpoint. Find the value of the variable.

13. Special Right Triangles
5.1
Special Right Triangles
Pg. 166, 5.1 #1-25