SPECIAL RIGHT

TRIANGLES

45o-45o-90o Triangle Theorem

• In a 45o-45o-90o triangle, both legs are congruent and the length of the hypotenuse is

times the length of a leg.

hypotenuse = x leg s

s

45o

45o

s

pg 262

Find the value of x.

a. b.

c.

x45o 45o

9

x

45o

45o

x

45o

45o

Relating to the Real World - Baseball

A baseball diamond is a square. The distance from base to base is 90ft. To the nearest foot, how far does the second baseman throw a ball to home plate?

30o-60o-90o Triangle Theorem• In a 30o-60o-90o triangle, the length of the hypotenuse

is twice the length of the shorter leg. The length of the longer leg is times the length of the shorter leg.

hypotenuse = 2 x shorter leg

hypotenuse = x shorter leg s

s

30o

60o

2s

pg 263

Find the value of x and y.1. 2.

3. 4.

x

y

4

30o

xy

1230o 60o

x

y60o

xy

60o

Altitude TheoremThe altitude of an equilateral

triangle is times the length of its side.

pg 264

s

s

ss

For an isosceles right triangle or 45o-45o-90o triangle,

the lengths of the legs are equal.the length of the hypotenuse is

times the length of a leg.

pg 264

s

s

45o

45o

s

• the length of the hypotenuse is twice the length of the side opposite the 30o angle.

• the length of the side opposite the 60o angle is

times the length of the side opposite the 30o angle.

For a 30o-60o-90o triangle,

s

s

30o

60o

2s