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Date: Number:

Discovering the Pythagorean Theorem

You will now get the chance to discover one of the most important geometric equations yourselves! Using the ruler, measure each side of the triangle. Record your measurements under the appropriate sides. Then square each side. On the right hand side of the chart, record what relationship you see between the squared numbers.

**Round measurements to the nearest centimeter**Triangl

eLeg (cm)

Leg (cm)

Hypotenuse (cm)

What relationship do you see using the squared numbers?

1

Squared

2

Squared

3

Squared

4

Squared

5

Squared

The Pythagorean Theorem tells us something about the

relationship between the sides of a right triangle. Review your

chart. What patterns do you see between the squares of the

sides. Take a guess at what the Pythagorean Theorem tells us:

___________________________

Pythagorean Theorem: For right triangles where: a c

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Date: Number:

bBut how do we actually use the Pythagorean Theorem?

For a triangle with a=9, b=12, and c unknown. To find c:

1. Substitute 9 for a and 12 for b in the Pythagorean Theorem: 9 c

( )2 + ( )2 = c2

2. Simplify: 12 81 + = c2

3. Take the square root of both sides:

√306= √ c2

4. You have now solved for c, the hypotenuse:

C=

For a triangle with a known, b unknown, and hypotenuse known:

1. Substitute the side measurements for the variables.

(16) 2 + b2 = (20) 2

2. Simplify: 12 20

(256) + b = b3. Isolate variable on one side:

(256) + b =400

b=

4. Take the square root of both sides:

√b = √144

b=

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Date: Number:

Find the missing side length to complete the table. Round your answers to the nearest tenth.

Pythagorean Theorem: a2 + b2 = c2

Right

Triangl

e

Length

of Leg

Length

of Leg

Length of

Hypotenu

se

1 9 12

2 16 20

3 15 25

4 18 30

5 9.3 8

6 4.7 12.5

7 5.1 23.2

Find the missing side length in the right triangles drawn below.

11. 12.

6.7 cm 5.2 cm

12.8 m

5.9 m