Special Right Triangles
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Special Right Triangles
description
Special Right Triangles. Words to Know:. 45 ◦ -45 ◦ -90 ◦ Triangle Theorem. Look. 30 ◦ -60 ◦ -90 ◦ Triangle Theorem. special right Triangles. 45 ◦ -45 ◦ -90 ◦ Special Right Triangles . a 2 + b 2 = c 2. Look!. 45 ◦. 1 2 + 1 2 = y 2. y. 1. x. 1 + 1 = y 2. 45 ◦. 2 = y 2. x. 1. - PowerPoint PPT Presentation
Transcript of Special Right Triangles
Special Right Triangles
Words to Know:45◦-45◦-90◦ Triangle Theorem
30◦-60◦-90◦ Triangle Theorem
Look
special right Triangles
45◦-45◦-90◦ Special Right Triangles
Look
!
45◦
45◦
x
x y
a2 + b2 = c212 + 12 = y2
2 = y2
2 = y
1
1
1 + 1 = y2
45◦-45◦-90◦ Triangle Theorem
In a 45◦-45◦-90◦ triangle, both legs are congruent, and the length of the hypotenuse is the length of a leg times .
45◦
45◦
l
ll 2
Wri
te
2
Example #1:
You
Try!
Find the value of x.
45◦
17
x
x = 17 2
To find the length of one leg…
Know
Th
is!
If you were given the hypotenuse of a 45-45-90 triangle, to find the length of one of the legs, all you need to do is divide the hypotenuse by 2, then multiply by .
2
Example #4:
You
Try!
Find the value of x.
45◦
x
20
x= 210
4102210 210
20
Chec
k!
45◦-45◦-90◦ Triangle Theorem W
rite
!
45◦
45◦
Length of a Leg Hypotenuse
34718
232427218
50 25060230
5 2
5
5
x =
Deriving the 30◦-60◦-90◦ Triangle Theorem Lo
ok!
30◦
60◦ 60◦
60◦
2
2 2
1
a2 + b2 = c2
x2 + 12 = 22
x2 + 1 = 4x2 = 3
x = 33
x
Wri
te!
x =
Deriving the 30◦-60◦-90◦ Triangle Theorem Lo
ok!
30◦
60◦ 60◦
60◦
8
8 8
4
a2 + b2 = c2
x2 + 42 = 82
x2 + 16 = 64x2 = 48x = 316
34
x
30◦-60◦-90◦ Triangle Theorem W
rite
!
30◦
60◦
s
3s2s
The HYPOTENUSE is 2 times the shorter leg.
3The LONGER LEG is times the shorter leg.
45◦-45◦-90◦ Triangle Theorem W
rite
!
45◦
45◦
Length of a Leg Hypotenuse
55 2
5
Length of a Leg Hypotenuse
69
1116
2629211216
2103020
215
Makes sense, now…?
30◦-60◦-90◦ Triangle Theorem Re
ad
In a 30◦-60◦-90◦ triangle, the length of the hypotenuse is twice the length of the shorter leg. The length of the longer leg is times the length of the shorter leg.
3 30◦
60◦
s
3s2s
Example #1:
You
Try!
Find the value of x and y.
30◦
60◦
x
y22 x = 11311y
30◦-60◦-90◦ Special Right TrianglesYo
u Tr
y!
a(short leg)
1 31b
60◦
30◦
a
c
c(hypotenuse)
b(longer leg)
22 3245 3510
12 3122420 3204030 33060
You Try!
30o
60o
45o
45o
1.
2. 3.
4.
Find the value of each side.
5 cm
5 cm
10 cm
cm 25
cm 35
30o
60o
45o
45o cm
Any Questions…?
Classwork
Classwork Rocks!Oh, yeah!
ObjectiveObjective:– understand and use the properties of special right
triangles.
– Students know and are able to use angle and side relationships in problems with special right triangles, such as 30◦- 60◦ - 90◦ triangles and 45◦- 45◦ - 90◦ triangles.
Look
!
