lesson 10: special right triangles
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Lesson 10:Lesson 10:Special Special Right Right
TrianglesTrianglesMoody Mathematics
Take a Take a square…square…
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Find its Find its diagonaldiagonal
Here Here it isit is
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Find its Find its lengthlength
xx dd
xx Moody Mathematics
xx dd
xx
2 2 2x x d 2 22x d
2 22x d
2x d
2 2x d
Moody Mathematics
Summarize Summarize the pattern:the pattern:
Moody Mathematics
4545oo-45-45oo-90-90oo
legleg lelegg
lelegg
2
Moody Mathematics
4545oo-45-45oo-90-90oo
66 66
66
2
Moody Mathematics
Practice:Practice:
Moody Mathematics
4545oo-45-45oo-90-90oo
88 88
88
2
Moody Mathematics
4545oo-45-45oo-90-90oo
55 55
55
2
Moody Mathematics
4545oo-45-45oo-90-90oo
1010 1010
1010
2
Moody Mathematics
4545oo-45-45oo-90-90oo
2 22
2Moody Mathematics
4545oo-45-45oo-90-90oo
3 2
3 2
6
Moody Mathematics
8
4 2 4 2
4545oo- 45- 45oo--9090oo
Moody Mathematics
4545oo-45-45oo-90-90oo
10 2
10 2
20
Moody Mathematics
Now Let’s Now Let’s take an take an Equilateral Equilateral Triangle…Triangle…
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… … Find its Find its AltitudeAltitude
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xx xx
xx
aa
2 2
x x
22 2
2
xa x
22 2
4
xa x
2 22 4
4 4
x xa
22 3
4
xa
Moody Mathematics
xx xxaa
2 2
x x
22 3
4
xa
22 3
4
xa
3
2
xa
2 3
4
xa
Moody Mathematics
Summarize Summarize the pattern:the pattern:
Moody Mathematics
3030oo-60-60oo-90-90oo
Hypotenu
Hypotenusese
Longer Longer legleg
Short
er
Short
er
Leg
Leg 30
60
Moody Mathematics
3030oo-60-60oo-90-90oo
Hyp.Hyp.
½ Hyp. ½ Hyp.
½ H
yp
.½
Hyp
.
30
60
3Moody Mathematics
3030oo-60-60oo-90-90oo
30
60
10 3
2010
Moody Mathematics
Practice:Practice:
Moody Mathematics
3030oo-60-60oo-90-90oo
30
60
14 3
2814
Moody Mathematics
3030oo-60-60oo-90-90oo
30
60
8 3
168
Moody Mathematics
3030oo-60-60oo-90-90oo
30
60
9 3
189
Moody Mathematics
3030oo-60-60oo-90-90oo
30
60
3
21
Moody Mathematics
3030oo-60-60oo-90-90oo
30
60
3 3
63
Moody Mathematics
3030oo-60-60oo-90-90oo
30
60
73
2
77
2
Moody Mathematics
3030oo-60-60oo-90-90oo
30
60
2 3
42
Moody Mathematics
3030oo-60-60oo-90-90oo
30
60
93
2
99
2
Moody Mathematics
3030oo-60-60oo-90-90oo
30
60
6
4 32 3
Moody Mathematics
3030oo-60-60oo-90-90oo
30
60
12
8 34 3
Moody Mathematics
Review Review Both Both
Patterns:Patterns:Moody Mathematics
4545oo-45-45oo-90-90oo
legleg lelegg
lelegg
2
Moody Mathematics
3030oo-60-60oo-90-90oo
Hyp.Hyp.
½ Hyp. ½ Hyp.
½ H
yp
.½
Hyp
.
30
60
3Moody Mathematics
Mixed Mixed Practice:Practice:
Moody Mathematics
30
60
12 3
2412
Moody Mathematics
30
60
3 3
63
Moody Mathematics
88 88
88
2
Moody Mathematics
1010 1010
1010
2
Moody Mathematics
30
60
3
21
Moody Mathematics
10
10
105 3
Moody Mathematics
30
60
15 3
3015
Moody Mathematics
8 8
8
8
8 2
Moody Mathematics
30
60
8 3
16 8
Moody Mathematics
8
4 2 4 2
Moody Mathematics
30
60
3 3
63
Moody Mathematics
15
15
15 2
15
15
Moody Mathematics
30
60
15
10 35 3
Moody Mathematics
30
60
12
8 34 3
Moody Mathematics
44
44
4 2
Moody Mathematics
2 22
2Moody Mathematics
18
18
189 3
Moody Mathematics
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