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Pythagorean Theorem
Module 6 – Lesson 6
2

2

2

The Pythagorean Theorem: a + b = c

The square of one leg (a) plus the square of the other leg (b) is equal to the square of the hypotenuse (c)
Hypotenuse:

Legs:

Right triangle:

The longest side of a right

The two shorter sides of a right

triangle; side opposite from the

triangle; the sides that meet at 90

right angle
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2

2

A triangle with a 90-degree angle
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Commonly used Pythagorean triples:
∑

3 4 5

∑

8 15 17

∑

5 12 13

∑

9 40 41

∑

7 24 25

Remember that you can create other triples by multiplying each number in a given triple by the same number
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∑

Ordered pair: A coordinate or point written in the form of (x, y)
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∑

x-axis: The horizontal number line of the coordinate plane
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∑

Two dimensional (2D): An object that has width and length but no thickness (depth); examples include
squares, circles, and triangles
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RULE
Distance on a Number Line
On a number line, the distance between points a and b is |a − b|
When the points lie on a line that is neither vertical nor horizontal, we cannot count or use a formula to find
the distance
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∑

Step 2: Draw vertical and horizontal line segments to create a right triangle with the diagonal as the
hypotenuse
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∑

Step 4: Use the Pythagorean Theorem to find the length of the hypotenuse
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Base: The surface on which an object rests
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∑

Height:

The vertical distance from top to bottom that creates a 90degree angle with the base
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EX
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Apply the volume formula:
2

∑

V = πr h

∑

V = π (3) (12)

∑

V = (3
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12 in

3

Cone: a three-dimensional object that has a circular base and tapers to a point at the other end

What do the formulas have in common?
∑

2

They both contain the πr h part, but the cone also has a
1

fraction of /3
∑

Their formulas are very similar because the shapes are
1

also similar
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14)(12) (19)

∑

V = /3(3
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04)

1

2

1
1

1

Note: Once you have worked this far, you need to multiply by /3
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∑

Instead, just divide by 3 or multiply by /3 to get your final answer
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3333 or some approximation of the fraction, your answer will not be accurate
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04) =

8591
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68 in

So the volume of the cone is 2863
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∑

They all have pi
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∑

The cylinder and cone formulas square the

radius, but the sphere formula cubes it
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What is the volume of a sphere with a radius of 6 centimeters?
Apply the volume formula:
4

3

∑
∑

V = /3(3
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14)(216)

∑
∑

V = /3πr

V = /3(678
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Put a 1 underneath
the product so that you can multiply
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24

V = /3(678
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4

3

678
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96

/3 = 904
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32 cm

3



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