Pythagorean Theorem 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 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

How can you determine if three side lengths form a right triangle using the Pythagorean Theorem?

Back

To determine if three side lengths (a, b, c) form a right triangle, identify the longest side (hypotenuse) and check if a² + b² = c² holds true.

Front

What are the side lengths of a right triangle?

Back

In a right triangle, the side lengths consist of two legs (the sides that form the right angle) and one hypotenuse (the side opposite the right angle).

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 equals 10².

Front

What is the significance of the longest side in a triangle when applying the Pythagorean Theorem?

Back

The longest side in a triangle is considered the hypotenuse when determining if the triangle is a right triangle using the Pythagorean Theorem.

Front

Can the side lengths 15, 30, and 34 form a right triangle?

Back

No, because 15² + 30² = 225 + 900 = 1125, which does not equal 34² (1156).

Front

What is a right triangle?

Back

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

Front

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

Back

In a right triangle, the sum of the squares of the lengths of the two legs equals the square of the length of the hypotenuse.

Front

If a triangle has sides of lengths 13, 80, and 81, does it form a right triangle?

Back

No, because 13² + 80² = 169 + 6400 = 6569, which does not equal 81² (6561).