Geometry Warm-Up 1/31/12
Find the value of x.
13
7
x
x12
151.
2.
Perfect Squares Quiz
12. 142
2. 172
3. 122
4. 52
5. 82
6. 192
7. 112
8. 12
9. 202
10. 162
11. 72
1. 42
13. 22
14. 102
15. 32
16. 182
17. 132
18. 92
19. 152
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.
45
45
A
B
C
30
60
E
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
as each legHypotenuse = √2 ● leg
45
45 hypotenuse
leg
leg
30-60-90 Triangles Special Relationships
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 legLong Leg = √3 ● short leg
hypotenuse
short leg
long leg
30
60
E
F D
Example 1
Find the value of x.
7
x
7
45
Hypotenuse = √2 ● leg
x = √2 (7)
x = 7√2
Example 2
Find the values of s and t.
30
t
s
9
Long leg = √3 ● short leg
9 = √3 (s)
9√3 = s
3 3√3 = s
Hyp = 2 ● short leg
t = 2 (3√3)
t = 6√3
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