Special Right Triangles

- We make a living by what we get, but we make a

life by what we give. -- Winston Churchill

- Chapter 8 Section 3
- Learning Goal Use properties of 45-45 -90 ,

and - 30 -60 -90 Triangles

45-45-90 Triangles

x

- Special Right Triangle

45

d2 x2 x2

d

x

d2 2x2

Simplify

vd2 v 2x2

d xv 2

Three sides of lengths x, x, xv2

What did we learn about ratios of sides?

Ratio of a 45-45-90 triangle is

1 1 v2

45-45-90 Triangles

- Find the missing side

6

a 4v2 cm

45-45-90 Triangles

3

8

45

21

14

Special Right Triangles

A 24.5 mm

30-60-90 Triangles

Consider an equilateral ?

30

a2 (2x)2 x2

2x

2x

Simplify

a2 4x2 x2

a

a2 3x2

60

60

va2 v3x2

x

x

a xv3

Three sides of lengths x, 2x, xv3

Ratio of a 30-60-90 triangle is

Ratios of sides?

1 v3 2

30-60-90 Triangles

- Find the missing sides

4

60

10

5

8v3 3

30

5v3

30-60-90 Triangles

60

30

8

6

60

4v2

Find the Altitude of the ?

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, 30-60-90