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

45°-45°-90° Triangles Special Right Triangle

x

x d d2 = x2 + x2

d2 = 2x2Simplify:

√d2 = √ 2x2

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°

45°-45°-90° Triangles

Find the missing side

a = 4√2 cm

6√245°

6

45°-45°-90° Triangles

38

45°21

14

Special Right TrianglesWALLPAPER 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

30°-60°-90° TrianglesConsider an equilateral ∆

2x

x

2x

x

a

60° 60°

30°

a2 = (2x)2 – x2

Simplify: a2 = 4x2 – x2

a2 = 3x2

√a2 = √3x2

a = x√3Three sides of lengths x, 2x, x√3

Ratios of sides?

Ratio of a 30°-60°-90° triangle is:

1 : √3 : 2

30°-60°-90° Triangles

Find the missing sides

60°

30°5

10

5√3

8√33

4

30°-60°-90° Triangles

68

30°

4√2

60°

60°

Find the Altitude of the Δ

Special Right Triangles

Refer to the figure. Find x and y.

Special Right Triangles

60 cm

The length of the diagonal of a square is cm. Find the perimeter of the square.

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, 30-60-90