Pythagorean Theorem Review The Pythagorean Theorem states in any right triangle the square of the hypotenuse is equal to the sum of the squares of the other two sides a 2 b 2 c ID: 728475
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Slide1
Using the Pythagorean Theorem in 3-Dimensional ShapesSlide2
Pythagorean Theorem Review
The Pythagorean Theorem states: in any right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides. a2
+ b
2
= c2Find the length of AC in thediagram below:
c
b
a
a
2
+ 5
2
= 13
2
a
2
+ 25 = 169
a
2
= 144
a = 12 Slide3
3-Dimensional Figures
How would you find the length of segment AV?Do you see a right triangle inside the shape?How would you find the length of
segment AF
?
Do you see the right triangle inside the shape?
5 m
12 mSlide4
To Find the Diagonal of a 3D Prism
Diagonals of prisms have a different formula(length)2 + (width)
2
+ (height)
2 = (diagonal of prism)2To Find the slant height of a cone or pyramid3D Figures
It doesn’t matter that it is 3D, there is a right triangle hidden in the problem
The slant height is just the hypotenuse of a right triangle.
Use a
2
+ b
2
= c
2Slide5
Use the Pythagorean Theorem to find the length of diagonal AF.
AF is the diagonal going through a prism. To find
AF
, we use the Pythagorean Theorem
differently.To find AF we need to know the length, width and height of the prism (because it is a 3D shape, we need 3 measurements) What is the length = AB?What is the width = FG?What is the height =
GB?(length)2 + (width)2 + (height)
2 = (diagonal of prism)26
2 + 22 + 32
= d236 + 4 + 9 = d2
49 = d27 = d
6cm
G
6
cm
2 cm
3 cm
The length of the diagonal AF is 7 cm.Slide6
Use the Pythagorean Theorem to find the length of diagonal TX.
TX
is the diagonal going through a prism.
To find
TX, we use the Pythagorean Theorem differently.What is the length = TU?What is the width = XW?What is the height = UW?(length)
2 + (width)2 + (height)2 = (diagonal of prism)2
122 + 62 +
92 = d2144 + 36 + 81 = d
2261 = d2
= d
12 in
6 in
9 in
The length of the diagonal TX is
which is between 16 and 17 inches.