8-2 Special Right Triangles

1
8-2Special Right Triangles

• Objective
• To use the properties of 450-450-900 and
  300-600-900 triangles

2
Review
a
Hypotenuse
Side c
c
Sides a and b
Legs
b
Pythagorean Theorem Given a right triangle then
____________
a2 b2 c2
Converse
Given 3 sides of triangle that satisfy
_____________________________
a2 b2 c2
then triangle is a right triangle
3
Right Triangle
450 450 900
Copy and Complete the table. Write answers in
radical form - no decimals.
450
Leg Hypotenuse
3
8
5
x
450
Theorem 8-5 In a ____________triangle, both
legs are congruent and the length of the
hypotenuse is_____. Hypotenuse ( )leg
450 450 900
4
300- 600- 900 Triangle
Copy and Complete the table. Write answers in
radical formno decimals
Shorter leg (a) Longer leg (b) Hypotenuse(c)
4
3
8
x
300
8
c
b
6
16
600
2x
a
Theorem 8-6 300-600-900 Triangle In 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)
5
Examples
Find the missing value.
7
c
6
300
a
d
12
d
b
c
8-2 p.503 7-12, 15-20
23