Pythagorean Theorem (Finding the Hypotenuse)

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 type of triangle does the Pythagorean Theorem apply to?

Back

The Pythagorean Theorem ONLY works on right triangles.

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

What is the formula for finding the hypotenuse?

Back

The formula is 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: 13² = 5² + b²; 169 = 25 + b²; b² = 144; b = 12.

Front

What is the length of the hypotenuse if both other sides are equal to 7?

Back

Using the Pythagorean Theorem: c² = 7² + 7²; c² = 49 + 49; c² = 98; c = √98 ≈ 9.9.

Front

What is a right triangle?

Back

A right triangle is a triangle that has one angle measuring 90 degrees.

Front

If a triangle has sides of lengths 3, 4, and 5, is it a right triangle?

Back

Yes, because 3² + 4² = 5² (9 + 16 = 25).

Front

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

Back

In a right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides.

Front

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

Back

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