c is always the hypotenuse — opposite the right angle, always the longest side.

How do I know whether to add or subtract?

Finding hypotenuse: add (a² + b² = c²). Finding a leg: subtract (a² = c² − b²).

What are Pythagorean triples?

Integer sets satisfying a² + b² = c², like (3,4,5) and (5,12,13). Worksheets use these for clean answers.

Pythagorean Theorem Worksheet

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Pythagorean Theorem Worksheet

Name:Date:Class:

1.A right triangle has sides

a = 7

and

b = 24

. Find the hypotenuse

c

Diagram not to scale

2.A right triangle has sides

b = 12

and

c = 13

. Find side

a

Diagram not to scale

3.A right triangle has sides

b = 12

and

c = 13

. Find side

a

Diagram not to scale

4.A right triangle has sides

a = 8

and

b = 15

. Find the hypotenuse

c

Diagram not to scale

5.A right triangle has sides

a = 7

and

b = 24

. Find the hypotenuse

c

Diagram not to scale

6.A right triangle has sides

a = 8

and

b = 15

. Find the hypotenuse

c

Diagram not to scale

7.A right triangle has sides

a = 5

and

c = 13

. Find side

b

Diagram not to scale

8.A right triangle has sides

b = 8

and

c = 10

. Find side

a

Diagram not to scale

9.A right triangle has sides

b = 15

and

c = 17

. Find side

a

Diagram not to scale

10.A right triangle has sides

a = 5

and

b = 12

. Find the hypotenuse

c

Diagram not to scale

11.A right triangle has sides

b = 15

and

c = 17

. Find side

a

Diagram not to scale

12.A right triangle has sides

a = 3

and

b = 4

. Find the hypotenuse

c

Diagram not to scale

13.A right triangle has sides

a = 8

and

b = 15

. Find the hypotenuse

c

Diagram not to scale

14.A right triangle has sides

b = 8

and

c = 10

. Find side

a

Diagram not to scale

15.A right triangle has sides

a = 5

and

b = 12

. Find the hypotenuse

c

Diagram not to scale

16.A right triangle has sides

a = 5

and

b = 12

. Find the hypotenuse

c

Diagram not to scale

17.A right triangle has sides

a = 7

and

c = 25

. Find side

b

Diagram not to scale

18.A right triangle has sides

a = 3

and

c = 5

. Find side

b

Diagram not to scale

19.A right triangle has sides

a = 5

and

b = 12

. Find the hypotenuse

c

Diagram not to scale

20.A right triangle has sides

b = 24

and

c = 25

. Find side

a

Diagram not to scale

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Worked Example

Problem: Right triangle with legs 9 cm and 12 cm. Find the hypotenuse.

9² + 12² = c²— Apply the theorem.
81 + 144 = 225 = c²— Square and add.
c = √225 = 15 cm— Take the square root.

Answer: 15 cm

Pythagorean Theorem Worksheet

Pythagorean Theorem Worksheet

Answer Key

Worked Example

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