geometry 8.4 special right triangles this is a very important section, as it is used extensively...
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Geometry
8.4 Special Right TrianglesThis is a very important section, as it is used extensively throughout the second semester.
All you need to know is how to multiply by root two and divide by root two.
45-45-90 Triangles
45o
45o
x
x2x
Since all 45-45-90 triangles are similar, by AA Similarity Postulate, this formula works for all 45-45-90 triangles.
The formula.
Does it work for the Pythagorean Theorem?
2x
2x
45o
45o
x x?
2x = 2x ?
Yes!
222 2xxx
2 2
The Two Types of 45-45-90 Problems
23
6
6
45o
45o 33
Type 1: Given the length of a leg, solve for the other leg and hypotenuse.
45o
45o
What are the other two lengths?
What are the other two lengths?
26
12
32Multiply by root 2.
Multiply by root 2.
The Two Types of 45-45-90 Problems
38
64
45o
45o
7
Type 2: Given the length of the hypotenuse, solve for the two legs.
45o
45o
What are the other two lengths?
What are the other two lengths?
22
7
22
7
64
Shortcut:
Divide the length of the hypotenuseby 2 and multiply by to find the length of the leg.
2
Divide by root 2.
Divide by root 2.
2leg
16
10 2
I. 45-45-90
Solve leg leg
AB BC AC
1. 10
2. 6
3.
4. 8
5.
6. 6
A
leg
legB C
45
45
2leg
Let’s Try Some From the HW
P. 302 #18, 26 P. 288 #28
HW P. 302 (1-8, 17, 18, 23, 26, 27) P. 288 #27-30 Quiz on Thursday Please sign up for School Loops(there is a link on my webpage) Answers to the packet below if you want to work them out:
310 ,65 4)
6 ,23 )3
103 ,103 )2
65 ,65 1)
IIIPart 2 Day
26 6, 6)
10 10, )5
24 ,24 )4
24 4,)3
23 ,23)2
210 10, 1)
IPart 1Day
26)2
25 x1)
III I
x
PartDay
Geometry
8.4 Special Right TrianglesPart 2This is a very important section, as it is used extensively throughout the second semester.
All you need to know is how to multiply and divide by two and multiply and divide by root three.
30-60-90 Triangles
60o
30o
x
2x
Since all 30-60-90 triangles are similar, by AA Similarity Postulate, this formula works for all 30-60-90 triangles.
The formula.
3x
Does it work for the Pythagorean Theorem?
2x
60o
30o 2x
x?
x + 3x = 4x ?
Yes!
2 2 3x
222 23 xxx
2
The Three Types of 30-60-90 Problems
35
6
30o
60o
5
10
Type 1: Given the length of the short leg, solve for the long leg and hypotenuse.
60o
30o
What are the other two lengths?
What are the other two lengths?
6223
Multiply by root 3.
Multiply by 2.
Multiply by root 3.
Multiply by 2.
The Three Types of 30-60-90 Problems
56
53
60o
30o
9
Type 2: Given the length of the hypotenuse, solve for the two legs.
30o
60o
What are the other two lengths?
What are the other two lengths?
2
9
32
9
153
Multiply by root 3.
Divide by 2.
Divide by 2.Multiply by root 3.
The Three Types of 30-60-90 Problems
3
65
2530
o
60o
9
Type 3: Given the length of the long leg, solve for the short leg and hypotenuse.
60o
30o
What are the other two lengths?
What are the other two lengths?
Shortcut:
Divide the length of the long legby 3 and multiply by to find the length of the short leg.
33
363
610
3
Multiply by 2.
Divide by root 3.
Multiply by 2
Divide by root 3.
3leg
3leg 2( )leg
4 3
B
A
2(leg)
leg C60
30
II. 30-60-90
Solve: leg
AB BC AC
1. 5
2. 8
3. 20
4. 8
5.
6. 12
6 ,36 6)
8 4, 5)
16 ,38 4)
10 ,310 )3
3
316 ,
3
38 2)
10 ,35 1)
II 1 PartDay
x
x
x
x 10
45 45
6
x60
9
x
III. Solve for x.
1. 2. 3.
Let’s Try A Few From the HW
P. 302 #20, #22 P. 288 #31
HWP. 302 (9-16) P. 302 (19-25, skip 23) P. 288 (31,32)
Quiz Friday
Here are the answers to your packet if you want to work them out.
6 ,36 6)
8 4, 5)
16 ,38 4)
10 ,310 )3
3
316 ,
3
38 2)
10 ,35 1)
II 1 PartDay
2
39)3
III 1
x
PartDay
2
57 ,
2
157 )6
23 ,63 )5
524 ,1512 )4
212 ,66 )3
3
610 ,
3
65 )2
220 ,210 1)
IVPart 2 Day