1. Geometry Mr. Jacob P. Gray Franklin County High School 8.2 Special Right Triangles Click for next Slide

2. 8.2 Special Right Triangles Click for next Slide Objectives To use the properties of 45˚-45˚-90˚ triangles To use the properties of 45˚-45˚-90˚ triangles To use the properties of 30˚-60˚-90˚ triangles To use the properties of 30˚-60˚-90˚ triangles

3. Essential Understanding Right Isosceles Triangle Take notes on the following: Take notes on the following: The acute angles of an Isosceles Right Triangle are both 45˚. Click for next Slide Certain right triangles have properties that allow you to use shortcuts to determine side lengths without using the Pythagorean Theorem. x x y 45˚ Another name for this is a 45˚-45˚-90˚ triangle. Use the Pythagorean Theorem Simplify Take the positive square root of each side

4. Theorem 8-5 45˚-45˚-90˚ Triangle Theorem Take notes on the following: Take notes on the following: In a 45˚-45˚-90˚ triangle, both legs are congruent and the length of the hypotenuse is √2 times the length of a leg. Click for next Slide s√2 45˚ s s Hypotenuse = √2 · leg

5. Problem 1) Finding the Length of the Hypotenuse Problem 1) Finding the Length of the Hypotenuse What is the value of each variable? Here is a problem to practice. Here is a problem to practice. Click for next Slide 9 h 45˚ 2√2 45˚ x 12 Hypotenuse = √2 · leg

6. Problem 2) Finding the Length of a Leg Problem 2) Finding the Length of a Leg x What is the value of x ? Here is another problem to practice. Here is another problem to practice. Click for next Slide x 45˚ 6 Hypotenuse = √2 · leg

7. Problem 3) Finding Distance Problem 3) Finding Distance Softball Softball A softball diamond is a square. The distance from base to base is 60 ft. To the nearest foot, how far does the catcher throw the ball from home to second base? Here is another problem to practice. Here is another problem to practice. Click for next Slide 60 ft Hypotenuse = √2 · leg d Use a calculator. The catcher throws the ball about 85 ft from home plate to second base.

8. Theorem 8-6 30˚-60˚-90˚ Triangle Theorem Another type of special right triangle is a 30˚-60˚-90˚ triangle. Another type of special right triangle is a 30˚-60˚-90˚ triangle. In a 30˚-60˚-90˚ triangle, the length of the hypotenuse is twice the length of the shorter leg. The length of the longer leg is √3 times the length of the shorter leg. Click for next Slide 2s 60˚ s s√3 30˚ hypotenuse = 2 · shorter leg longer leg = √3 · shorter leg

9. Problem 4) Using the Length of One Side Problem 4) Using the Length of One Side Algebra Algebra What is the value of d in simplest radical form? Here is a problem to practice. Here is a problem to practice. Click for next Slide f 60˚ 5 30˚ d

10. Problem 5) Applying the 30˚-60˚-90˚ Triangle Theorem Problem 5) Applying the 30˚-60˚-90˚ Triangle Theorem Jewelry Making Jewelry Making An artisan makes pendants in the shape of equilateral triangles. The height of each pendant is 18mm. What is the length s of each side of a pendant to the nearest tenth of a millimeter? Here is the last problem to practice. Here is the last problem to practice. Click for next Slide S 18mm Each side is about 20.8 mm long.

11. Classwork Pages 503-505 7-21 all 23-29 all 34, 35, 37, 38, 39 STOP