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). It can be expressed as: a² + b² = c².

Front

What is a right triangle?

Back

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

Front

What is the hypotenuse in a right triangle?

Back

The hypotenuse 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 is 8, what is the length of the hypotenuse?

Back

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

Front

Can the lengths 5, 12, and 13 form a right triangle?

Back

Yes (5² + 12² = 25 + 144 = 169 = 13²).

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 the lengths of the sides of a triangle are 7, 24, and 25, does it form a right triangle?

Back

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

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, where c is the hypotenuse.

Front

True or False: The hypotenuse is always the shortest side of a right triangle.

Back

False (The hypotenuse is always the longest side of a right triangle).

Front

In construction, why are right triangles important?

Back

Right triangles are used in construction to ensure structures are level and stable.