Pythagorean Theorem Basics - Grade 6
Explore the fundamentals of the Pythagorean Theorem with this Grade 6 worksheet, including identifying right triangles and applying the theorem to find missing side lengths.
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Pythagorean Theorem Basics
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Read each question carefully and answer to the best of your ability. Show all your work for full credit.
The Pythagorean Theorem describes the relationship between the three sides of a right triangle. It states that the square of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides (legs). This is written as: a² + b² = c²
1. Which of the following describes a right triangle?
A triangle with all sides equal.
A triangle with one angle measuring 90 degrees.
A triangle with two sides equal in length.
A triangle with all angles less than 90 degrees.
2. In a right triangle, the longest side, opposite the right angle, is called the .
3. The two shorter sides of a right triangle are called the .
4. A right triangle has legs measuring 3 cm and 4 cm. What is the length of the hypotenuse?
5. A ladder is 10 feet long and is leaning against a wall. The base of the ladder is 6 feet away from the wall. How high up the wall does the ladder reach?