Lesson 10:Lesson 10:Special Special Right Right

TrianglesTrianglesMoody Mathematics

Take a Take a square…square…

Moody Mathematics

Find its Find its diagonaldiagonal

Here Here it isit is

Moody Mathematics

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…

Moody Mathematics

… … Find its Find its AltitudeAltitude

Moody Mathematics

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