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). Formula: a² + b² = c².

Front

What is the converse of the Pythagorean Theorem?

Back

The converse of the Pythagorean Theorem states that if in a triangle, the square of the length of one side 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 5, 12, and 13, does it form a right triangle?

Back

Yes, because 5² + 12² = 25 + 144 = 169 = 13².

Front

If a triangle has sides of lengths 5, 6, and 10, does it form a right triangle?

Back

No, because 5² + 6² = 25 + 36 = 61, which is not equal to 10² (100).

Front

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

Back

No, because all sides are equal and do not satisfy the Pythagorean Theorem.

Front

If a triangle has sides of lengths 13, 35, and 36, does it form a right triangle?

Back

No, because 13² + 35² = 169 + 1225 = 1394, which is not equal to 36² (1296).

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

What are the legs of a right triangle?

Back

The legs of a right triangle are the two sides that form the right angle.

Front

How can you determine if three lengths can form a right triangle?

Back

Use the Pythagorean Theorem: check if a² + b² = c², where c is the longest side.

Front

What is an example of a Pythagorean triple?

Back

(3, 4, 5) is a Pythagorean triple because 3² + 4² = 9 + 16 = 25 = 5².