Geometry Section 9.4

Special Right Triangle Formulas

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

Two sides of a right triangle.

In section 9.2, we examine 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 24

2

28

4

28

2

2

24 24 yx

142 a

2

14a 27

2

214

4

214

2

2

27 27 yx

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

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

343

312

9

312

3

3

3

12

123

s

s

38342y 34 x

ss2

3s

3

8

83

s

s

3

38

9

38

3

3

3

316

3

382y

3

38x

Example: Find the length of the altitudes in an equilateral triangle that has sides of

length 20cm.

20

60

30

s

3ss2

10

202

s

s

310altitude