Pythagorean Converse

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 converse of the Pythagorean Theorem?

Back

The converse of the Pythagorean Theorem states that if the square of the length of one side of a triangle is equal to the sum of the squares of the lengths of the other two sides, then the triangle is a right triangle.

Front

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

Back

Yes, because 3² + 4² = 9 + 16 = 25, which is equal to 5².

Front

If a triangle has sides of lengths 6, 8, and 10, does it form a right triangle?

Back

Yes, because 6² + 8² = 36 + 64 = 100, which is equal to 10².

Front

If a triangle has sides of lengths 5, 12, and 13, does it form a right triangle?

Back

Yes, because 5² + 12² = 25 + 144 = 169, which is equal to 13².

Front

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

Back

Yes, because 7² + 24² = 49 + 576 = 625, which is equal to 25².

Front

If a triangle has sides of lengths 8, 15, and 17, does it form a right triangle?

Back

Yes, because 8² + 15² = 64 + 225 = 289, which is equal to 17².

Front

If a triangle has sides of lengths 10, 10, and 10, does it form a right triangle?

Back

No, because the triangle is equilateral and does not satisfy the Pythagorean Theorem.

Front

If a triangle has sides of lengths 9, 12, and 15, does it form a right triangle?

Back

Yes, because 9² + 12² = 81 + 144 = 225, which is equal to 15².

Front

What is the formula to check if three sides form a right triangle?

Back

To check if three sides a, b, and c form a right triangle, verify if a² + b² = c², where c is the longest side.