Honors Geometry Section 5.5

Special Right Triangle Formulas

What must we know in order to use the Pythagorean Theorem?

Two sides of a right triangle.

This note sheet examines two special right triangles. They are

special because we only need to know the length of 1 side to find the length of the other two sides.

45-45-90 or Isosceles Right TriangleIn a 45-45-90 triangle, the

hypotenuse is equal to the length of a leg times____.2

222 aac

22 2ac

222 22 aaac

2a

Examples: Find the length of x and y.

28

8

y

x

a

a

2a a

a

2a

82 a

2

8a

242

28

4

28

2

2

2

8a

24

24

y

x

In a 30-60-90 triangle, the hypotenuse equals two times the shorter leg and the longer leg equals the shorter leg times

.

3

s2

3s

Examples: Find the length of x and y.

s s

3s 3s

2s 2s

4

82

s

s

34

4

x

y 3

38

9

38

3

3

3

8s

3

8

83

s

s

3

316

3

382y

3

38x

Example: Find the perimeter of a square with diagonals of length 25cm.

25

45

45

90a

a2a

252 a

25.122

225

4

225

2

2

2

25a

cm250)25.12(4P