1. Special Right Triangles
OBJECTIVE:
To use the properties of triangles
BIG IDEAS: MEASUREMENT REASONING AND PROOF
ESSENTIAL UNDERSTANDING:
Certain right triangles have properties that allow their side lengths to be determined without using the Pythagorean Theorem
MATHEMATICAL PRACTICE:
Make sense of problems and persevere in solving them

2. Math Background
The study of the relationship of the lengths of the sides of the special right triangles provides a bridge between the study of the Pythagorean Theorem and the study of Trigonometry. The properties of right triangles and isosceles triangles, along with the Pythagorean Theorem, can be easily used to determine the ratios of the sides of triangles that contain acute angles of You will want to memorize the ratios of the sides in the special triangles because they provide shortcuts for finding lengths of sides.

3. Special Right Triangles
Triangle Theorem:
In a triangle, both legs are ____________________ and the length of the hypotenuse is
In a triangle, the length of the hypotenuse is _______________ the length of the _______________ leg. The length of the _____________ leg is

4. EX 1: Find the value of each variable

5. EX 1: Find the value of each variable

6. EX 1: Find the value of each variable

7. Finding distance
EX 2: A high school softball diamond is a square. The distance from base to base is 60 feet. To the nearest foot, how far does a catcher throw the ball from home plate to second base?

8. Finding distance
EX 3: An artisan makes pendants in the shape of equilateral triangles. The height of each pendant is 18mm. What is the length of each side of a pendant to the nearest tenth of a millimeter?

9. GEOM IXL Q4
Mastery Level