8-28-2Special Right TrianglesSpecial Right Triangles

Objective:Objective:

To use the properties of 45To use the properties of 4500-45-4500-90-9000 and 30and 3000-60-6000-90-9000 triangles triangles

Pythagorean TheoremGiven a right triangle then ____________

a

b

c

a2 + b2 = c2

Review

Hypotenuse:

Legs:

Converse:

Side c

Sides a and b

Given 3 sides of triangle that satisfy _____________________________

a2 + b2 = c2

then triangle is a right triangle

Right Triangle

Leg Hypotenuse

3

8

5

x

Theorem 8-5 In a ____________triangle, both legs are congruent and the length of the hypotenuse is_____.

Hypotenuse = ( )leg

Copy and Complete the table. Write answers in radical form - no decimals.

23

28

25

2x

2a

450

450

450 – 450 – 900

450 – 450 – 900

2

300- 600- 900 Triangle

a

300

600

Shorter leg (a)

Longer leg (b)

Hypotenuse(c)

4

3

8

x

Theorem 8-6 300-600-900 TriangleIn a 300-600-900 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(shorter leg)longer leg = (shorter leg)

3

Copy and Complete the table.

Write answers in radical formno decimals

34

33

38

3x

8

6

16

2x

b c

3

Examples

a

7

8-2 p.503: 7-12, 15-

20

Find the missing value.

b

23

27

2

23

c

300

d 12

c =

d =

6

36