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

Special Right Triangle d2 = x2 + x2 Simplify: d2 = 2x2 x 45 x d

d2 = 2x2 d = x 2 Three sides of lengths x, x, x2 What did we learn about ratios of sides? Ratio of a 45-4590 triangle is: 1 : 1 : 2 45-45-90 Triangles

Find the missing side 6 45 62 a = 42 cm 45-45-90 Triangles 3 8

45 14 21 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 454590 triangle measures

millimeters? A = 24.5 mm 30-60-90 Triangles 30 Consider an equilateral 2 2

2 a = (2x) x 2x 2x 2 2 2 Simplify: a = 4x x a a2 = 3x2 a2 = 3x2 60 60 x

x a = x3 Three sides of lengths x, 2x, x3 Ratios of sides? Ratio of a 30-6090 triangle is: 1 : 3 : 2 30-60-90 Triangles Find the missing sides

4 60 10 5 30 53 83 3 30-60-90 Triangles 60

6 8 60 Find the Altitude of the 30

42 Special Right Triangles Refer to the figure. Find x and y. Special Right Triangles The length of the diagonal of a square is cm. Find the perimeter of the square.

60 cm Special Right Triangles The side of an equilateral triangle measures 21 inches. Find the length of an altitude of the triangle. Homework Special Right Triangles 45-45-90, 3060-90