Free sample activity · Grades 6–8
Pythagorean Theorem Practice
Use this activity after learning squares and square roots. The Pythagorean theorem applies to right triangles; the side opposite the right angle is the hypotenuse.
6 questions · No account · No timer · Immediate feedback
Before you begin
How to use this activity
Allow five to ten minutes. Sketch each triangle, label the hypotenuse, and state the length unit after taking the square root. All lengths are positive.
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Put it into practice
Choose an answer, read the explanation, then move to the next question. Your answers stay in this page and are not saved.
In a right triangle with a² + b² = c², which side does c represent?
The hypotenuse is opposite the right angle and is the longest side of a right triangle. In this equation, it is c.
A right triangle has legs of 3 cm and 4 cm. How long is its hypotenuse?
The squared length is 3² + 4² = 9 + 16 = 25. Taking the positive square root gives 5 cm, not 25 cm.
A right triangle has legs of 5 m and 12 m. How long is its hypotenuse?
Compute 5² + 12² = 25 + 144 = 169. The positive square root is 13 m.
A right triangle has hypotenuse 10 cm and one leg 6 cm. How long is the other leg?
The missing leg squared is 10² - 6² = 100 - 36 = 64. Its positive length is 8 cm.
A triangle has sides of 6, 8, and 10 units. Is it a right triangle?
The longest side is 10. Since 36 + 64 = 100, the converse of the theorem shows that the triangle is right.
A rectangle is 9 units wide and 12 units long. What is the length of its diagonal?
Adjacent sides of a rectangle meet at a right angle. The diagonal squared is 9² + 12² = 225, so the diagonal is 15 units.
Practice complete
Draw a rectangle with sides of 9 and 12 units. Explain how its diagonal creates a right triangle and why the diagonal is 15 units.
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All questions, answers & explanations
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Identify the hypotenuse
In a right triangle with a² + b² = c², which side does c represent?
Answer: The side opposite the right angle
The hypotenuse is opposite the right angle and is the longest side of a right triangle. In this equation, it is c.
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Find a hypotenuse
A right triangle has legs of 3 cm and 4 cm. How long is its hypotenuse?
Answer: 5 cm
The squared length is 3² + 4² = 9 + 16 = 25. Taking the positive square root gives 5 cm, not 25 cm.
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A second triangle
A right triangle has legs of 5 m and 12 m. How long is its hypotenuse?
Answer: 13 m
Compute 5² + 12² = 25 + 144 = 169. The positive square root is 13 m.
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Find a missing leg
A right triangle has hypotenuse 10 cm and one leg 6 cm. How long is the other leg?
Answer: 8 cm
The missing leg squared is 10² - 6² = 100 - 36 = 64. Its positive length is 8 cm.
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Use the converse
A triangle has sides of 6, 8, and 10 units. Is it a right triangle?
Answer: Yes, because 6² + 8² = 10².
The longest side is 10. Since 36 + 64 = 100, the converse of the theorem shows that the triangle is right.
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A rectangle's diagonal
A rectangle is 9 units wide and 12 units long. What is the length of its diagonal?
Answer: 15 units
Adjacent sides of a rectangle meet at a right angle. The diagonal squared is 9² + 12² = 225, so the diagonal is 15 units.
Take it one step further
Draw a rectangle with sides of 9 and 12 units. Explain how its diagonal creates a right triangle and why the diagonal is 15 units.
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