Download Sec 9.4: Special Right Triangles

Geometry Warm-Up
1/31/12
 Find the value of x.
1.
2.
15
x
13
12
x
7
Perfect Squares Quiz
1.
2. 172
9. 202
17. 132
10. 162
18. 92
3. 122
11. 72
12. 142
19. 152
42
4.
52
82
5.
6. 192
7. 112
8. 12
13. 22
14. 102
15. 32
16. 182
20. 62
Sec 8.3: Special
Right Triangles
Geometry
January 31, 2012
Special Right Triangles
 Special Right Triangles

Triangles whose angles measures are
either 45-45-90 or 30-60-90.
E
B
60
45
45
C
30
A
F
D
45-45-90 Triangle
 Special Relationships
Because you have two 45 angles,
the two legs are congruent.
 The hypotenuse is √2 times as long
hypotenuse as each leg
Hypotenuse = √2 ● leg

45
leg
45
leg
30-60-90 Triangles
 Special Relationships

E

60
hypotenuse
short leg
30
F
Because the two acute angles have
different measures, you have a long leg
and a short leg
The hypotenuse is twice as long as the
short leg and the long leg is √3 times as
long as the short leg.
 Hypotenuse = 2 ● short leg
 Long Leg = √3 ● short leg
D
long leg
Example 1
 Find the value of x.
Hypotenuse = √2 ● leg
x
x = √2 (7)
45
x = 7√2
7
7
Example 2
Long leg = √3 ● short leg
 Find the values of s
9 = √3 (s)
9√3 = s
and t.
9
3
3√3 = s
30
s
t
Hyp = 2 ● short leg
t = 2 (3√3)
t = 6√3