1. Special Right Triangles Chapter 8 Section 3 Learning Goal: Use properties of 45°-45 °-90 °, and 30 °-60 °-90 ° Triangles  We make a living by what we get, but we make a life by what we give. -- Winston Churchill

2. 45°-45°-90° Triangles Special Right Triangle x x d d 2 = x 2 + x 2 d 2 = 2x 2 Simplify: √d 2 = √ 2x 2 d = x√ 2 Three sides of lengths x, x, x√2 What did we learn about ratios of sides? Ratio of a 45°-45°-90° triangle is: 1 : 1 : √2 45°

3. 45°-45°-90° Triangles Find the missing side a = 4√2 cm 6√2 45° 6

4. 45°-45°-90° Triangles 3 8 45° 21 14

5. Special Right Triangles WALLPAPER TILING The wallpaper in the figure can be divided into four equal square quadrants so that each square contains 8 triangles. What is the area of one of the squares if the hypotenuse of each 45°–45°– 90° triangle measures millimeters? A = 24.5 mm

6. 30°-60°-90° Triangles Consider an equilateral ∆ 2x x x a 60° 30° a 2 = (2x) 2 – x 2 Simplify: a 2 = 4x 2 – x 2 a 2 = 3x 2 √a 2 = √3x 2 a = x√3 Three sides of lengths x, 2x, x√3 Ratios of sides? Ratio of a 30°-60°-90° triangle is: 1 : √3 : 2

7. 30°-60°-90° Triangles Find the missing sides 60° 30° 5 10 5√3 8√3 3 4

8. 30°-60°-90° Triangles 6 8 30° 4√2 60° Find the Altitude of the Δ

9. Special Right Triangles Refer to the figure. Find x and y.

10. Special Right Triangles 60 cm The length of the diagonal of a square is cm. Find the perimeter of the square.

11. Special Right Triangles The side of an equilateral triangle measures 21 inches. Find the length of an altitude of the triangle.

12. Homework Special Right Triangles 45-45-90, 30-60-90