Special Right Triangles

Isosceles Right Triangles

45 – 45- 90

1

1

45o

45o

x

12 + 12 = x2

2 = x2

22 x

x2

x2

1

1

2

Ratio Leg:Leg:Hypotenuse 2:1:1

leg

leghypotenuse

Isosceles right triangles are all similar

1

1

2

Ratio Leg:Leg:Hypotenuse 2:1:1

leg

leghypotenuse

Ex. # 1 – Find the lengths of missing sides

5cm

x

y

1

1

2

511

5

x

x

25

21

5

y

y

30 – 60 – 90 Triangles

2

2

2

60o

30o

1

?x

12 + x2 = 22

3

32

x

x

x2 = 3

3

2hypotenuse

1short Leg

3long leg

60o

30o

Ratio, hypotenuse:short leg:long leg 3:1:2

30 – 90 – 60 triangles are all similar

2hypotenuse

1short Leg

3long leg

60o

30o

Ratio, hypotenuse:short leg:long leg 3:1:2

Ex. # 2 – Find the lengths of the missing sides

2hypotenuse

1short Leg

3long leg

60o

30o

7

x

y

1421

7

x

x

37

31

7

y

y

y 35

53

35

1

y

y

103

35

2

x

x

60o 30o

451/1-20432/32,35