special right triangles 45:45:90 right triangles
TRANSCRIPT
Special Right Triangles
45:45:90
Right Triangles
45:45:90 Relationship
Given: A square with side=4, find the length of the diagonal.
45º
45º
4
4
4
4
x
222 cba 222 44 c21616 c
2 32 cc 216
c24
24
Given: A square with side=10, find the length of the diagonal.
45º
45º
10
10
10
10
x
222 cba 222 1010 c2100100 c
2 200 cc 2100
c210
210
45:45:90 Relationship
Conclusion
3
2:: xxx
1 1
45º
45º
1
- The sides opposite the 45º angles are 1
- The side opposite the 90º angle is
- The ratio of the sides of a 45:45:90 right triangle is
22
Remember, the 45-45-90 triangle always has the same ratio for its sides:
2:1:1
90
45
45
Remember the relationship the sides have with the angles! The smallest side is across from the smallest angle!
4.12
Since 45 is the smallest angle, then the 1 goes across from it!
1
1
Since 90 is the largest angle, then the radical 2 goes across from it!
2
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Page 28
45 :45 : 901 :1: √24 :4 : 4√2
𝑦=4√2𝑥=4
Multiply by 4
Page 28
45 :45 : 901 :1: √23 :3 :3 √2
𝑦=3 √2𝑥=3
Multiply by 3
Page 28
45 :45 : 901 :1: √27 :7 :7 √2
𝑦=7 √2𝑥=7
Multiply by 7
Page 28
45 :45 : 901 :1: √2
:5√25 :5
𝑦=5𝑥=5
Multiply by 5
Page 28
45 :45 : 901 :1: √2
√2 :√2 :
𝑦=2𝑥=√2
Multiply by
√2 ∙√2=√ 4=2
2
Page 28
45 :45 : 901 :1: √22 :2 :2√2
2
45 :45 : 901 :1: √26 :6 :6 √2
6
45 :45 : 901 :1: √28 : 8 :8 √2
8
45 :45 : 901 :1: √21 :1:√2
1
45 :45 : 901 :1: √2
: 4
𝑠 ∙√2=4
𝑠 ∙ √2√2
= 4√2 𝑠=
4
√2
4
√2:
4
√2
Page 28
45 :45 : 901 :1: √2
6 :6 √2:
6 √2
45 :45 : 901 :1: √2
2 :2√2:
2√2
45 :45 : 901 :1: √215 :15√2:
15√2
45 :45 : 901 :1: √2
3√2 ::
3√2 ∙√2=¿3√ 4¿3 ∙2¿6
6
6
45 :45 : 901 :1: √2𝑠 :𝑠 √2:
𝑠√2
Page 28
45 :45 : 901 :1: √24 : 4: 4√2
4√2
4
𝑃=4 𝑠𝑃=4 ∙ 4𝑃=16
Page 28
45 45
902020
45 :45 : 901 :1: √2
20 :20 √220 :
20√220√2=28.28
¿28.3
Page 28
7
1545 90
45
74 4
45 :45 : 901 :1: √2
4 : 4√24 :4
15−7=882=4
Page 29
6
6
Homework
Page 29
Examples on top of page: #3,4
Exercises on bottom of page: #1,3,7,8,9
Separate Sheet
Page 29
8
8
45 :45 : 901 :1: √2
8 : 8√28 :8 √2
Page 29
A
D C
B45 90
45
12
45 :45 : 901 :1: √2
12 :12√21 2:12√2
Page 29
8
4
30
30 :60 : 901 :√3 :2
4
4 :𝑚𝑢𝑙𝑡𝑖𝑝𝑙𝑦𝑏𝑦 4
4√3 :8
8
Page 29
6030
9060
4√3
30 :60 : 901 :√3 :2: 4√3 :
𝑚𝑢𝑙𝑡𝑖𝑝𝑙𝑦𝑏𝑦 44 8
8
Page 29
8
46
60
9030
30 :60 : 901 :√3 :2
:6𝑚𝑢𝑙𝑡𝑖𝑝𝑙𝑦𝑏𝑦 3
3 :3 √3
𝐴𝑙𝑡𝑖𝑡𝑢𝑑𝑒=3
3
Page 29
45 90
45 45 :45 : 901 :1: √2
6 :6 √26 :66 √2
Page 29
12060
90305
30 :60 : 901 :√3 :2
:10𝑚𝑢𝑙𝑡𝑖𝑝𝑙𝑦𝑏𝑦 5
5 :5√3
10
5√3 5√3
5√3+5 √3=10 √3