Pythagorean Theorem Flashcard

Front

What is the Pythagorean Theorem?

Back

The Pythagorean Theorem states that in a right triangle, the square of the length of the hypotenuse (c) is equal to the sum of the squares of the lengths of the other two sides (a and b). It can be expressed as: c² = a² + b².

Front

What is the longest side of a right triangle called?

Back

The longest side of a right triangle is called the hypotenuse.

Front

If one side of a right triangle is 6 and the other side is 8, what is the length of the hypotenuse?

Back

Using the Pythagorean Theorem: c² = 6² + 8²; c² = 36 + 64; c² = 100; c = 10.

Front

True or False: The hypotenuse is always opposite the right angle in a right triangle.

Back

True.

Front

What is the formula to find the length of a side in a right triangle if the lengths of the other two sides are known?

Back

The formula is derived from the Pythagorean Theorem: a² + b² = c².

Front

If the hypotenuse is 13 and one side is 5, what is the length of the other side?

Back

Using the Pythagorean Theorem: 5² + b² = 13²; 25 + b² = 169; b² = 144; b = 12.

Front

What is the relationship between the sides of a right triangle?

Back

The relationship is defined by the Pythagorean Theorem, which states that the sum of the squares of the two shorter sides equals the square of the hypotenuse.

Front

In a right triangle, if one side is 9 and the hypotenuse is 15, what is the length of the other side?

Back

Using the Pythagorean Theorem: 9² + b² = 15²; 81 + b² = 225; b² = 144; b = 12.

Front

What does it mean if a triangle does not satisfy the Pythagorean Theorem?

Back

If a triangle does not satisfy the Pythagorean Theorem, it is not a right triangle.

Front

If a triangle has sides of lengths 7, 24, and 25, is it a right triangle?

Back

Yes, because 7² + 24² = 25² (49 + 576 = 625).