9.2_Special_right_triangles. PowerPoint Presentation

A special right triangle is a right triangle with some regular feature that makes calculations on the triangle easier, or for which simple formulas exist. For example, a right triangle may have angles that form simple relationships, such as 45°–45°–90°. This is called an "angle-based" right triangle.

1. 9.2 Special Right 9.2 Special Right
TrianglesTriangles
45-45-9045-45-90
EQ: What are the relationships between EQ: What are the relationships between
the sides on a 45 -45-90 triangle?the sides on a 45 -45-90 triangle?
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2. Take a square…Take a square…
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3. Find its diagonalFind its diagonal
Here Here
it isit is
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4. Find its Find its lengthlength
xx dd
xx Moody Mathematics

5. xx dd
xx
2 2 2
x x d 
2 2
2x d
2 2
2x d
2x d
2
2x d
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6. Summarize the Summarize the
pattern:pattern:
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7. 4545
oo
-45-45
oo
-90-90
oo
legleg
legleg
legleg
2
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8. 4545
oo
-45-45
oo
-90-90
oo
66
66
66
2
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9. 4545
oo
-45-45
oo
-90-90
oo
88
88
88
2
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10. 4545
oo
-45-45
oo
-90-90
oo
55
55
55
2
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11. 4545
oo
-45-45
oo
-90-90
oo
1010
1010
1010
2
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12. 4545
oo
-45-45
oo
-90-90
oo
222
2
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13. 4545
oo
-45-45
oo
-90-90
oo
32
32
6
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14. 8
4 2 4 2
4545
oo
- 45- 45
oo
-90-90
oo
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15. 4545
oo
-45-45
oo
-90-90
oo
102
10 2
20
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16. 9.2 Special Right
Triangles 30-60-90
Triangles
EQ: How do I find the lengths of sides of a
30-60-90 triangle

17. Now Let’s take Now Let’s take
an Equilateral an Equilateral
Triangle…Triangle…
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18. … … Find its AltitudeFind its Altitude
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19. xx xx
xx
aa
2 2
x x
2
2 2
2
x
a x
 
 
 
 
2
2 2
4
x
a x 
2 2
24
4 4
x x
a 
2
23
4
x
a
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20. xx xx
aa
2 2
x x
2
23
4
x
a
2
23
4
x
a
3
2
x
a
2
3
4
x
a
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21. Summarize the Summarize the
pattern:pattern:
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22. 3030
oo
-60-60
oo
-90-90
oo
H
y
p
o
te
n
u
se
H
y
p
o
te
n
u
se
Longer legLonger legS
h
o
r
t
e
r
L
e
g
S
h
o
r
t
e
r
L
e
g
30

60

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23. 3030
oo
-60-60
oo
-90-90
oo
H
y
p
.
H
y
p
.
½ Hyp. ½ Hyp.
½
H
y
p
.
½
H
y
p
.
30

60

3
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24. 3030
oo
-60-60
oo
-90-90
oo
30

60

103
20
10
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25. Practice:Practice:
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26. 3030
oo
-60-60
oo
-90-90
oo
30

60

143
28
14
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27. 3030
oo
-60-60
oo
-90-90
oo
30

60

83
16
8
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28. 3030
oo
-60-60
oo
-90-90
oo
30

60

93
18
9
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29. 3030
oo
-60-60
oo
-90-90
oo
30

60

3
2
1
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30. 3030
oo
-60-60
oo
-90-90
oo
30

60

33
6
3
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31. 3030
oo
-60-60
oo
-90-90
oo
30

60

7
3
2
7
7
2
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32. 3030
oo
-60-60
oo
-90-90
oo
30

60

23
4
2
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33. 3030
oo
-60-60
oo
-90-90
oo
30

60

9
3
2
9
9
2
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34. 3030
oo
-60-60
oo
-90-90
oo
30

60

6
43
23
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35. 3030
oo
-60-60
oo
-90-90
oo
30

60

12
83
43
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36. Review Both Review Both
Patterns:Patterns:
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37. 4545
oo
-45-45
oo
-90-90
oo
legleg
legleg
legleg
2
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38. 3030
oo
-60-60
oo
-90-90
oo
H
y
p
.
H
y
p
.
½ Hyp. ½ Hyp.
½
H
y
p
.
½
H
y
p
.
30

60

3
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39. Mixed Mixed
Practice:Practice:
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40. 30

60

123
24
12
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41. 30

60

33
6
3
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42. 88
88
88
2
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43. 1010
1010
1010
2
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44. 30

60

3
2
1
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45. 10
10
10
53
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46. 30

60

153
30
15
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47. 8 8
8
8
82
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48. 30

60

83
16
8
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49. 8
4 2 4 2
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50. 30

60

33
6
3
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51. 15
15
152
15
15
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52. 30

60

15
103
53
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53. 30

60

12
83
43
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54. 44
44
4 2
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55. 222
2
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56. 18
18
18
93
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