Pythagorean Theorem

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). Formula: a² + b² = c².

Front

What does side c represent in a right triangle?

Back

Side c represents the hypotenuse, which is the longest side of a right triangle, opposite the right angle.

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 the longest side in a right triangle.

Back

True.

Front

What is the formula to find the length of a missing side in a right triangle?

Back

Use the Pythagorean Theorem: a² + b² = c².

Front

If a right triangle has sides of length 5 and 12, what is the length of the hypotenuse?

Back

c = √(5² + 12²) = √(25 + 144) = √169 = 13.

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: b² = c² - a²; b² = 15² - 9²; b² = 225 - 81; b² = 144; b = 12.

Front

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

Back

The sum of the squares of the two shorter sides equals the square of the longest side (hypotenuse).

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).

Front

How can you determine if a triangle is a right triangle using the Pythagorean Theorem?

Back

If a² + b² = c² holds true for the lengths of the sides, then the triangle is a right triangle.