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: a² + b² = c².

Front

What is the Converse of the Pythagorean Theorem?

Back

The Converse of the Pythagorean Theorem states that if a triangle has side lengths a, b, and c, and a² + b² = c², then the triangle is a right triangle.

Front

Given the lengths 6 in, 8 in, and 10 in, does this form a right triangle?

Back

Yes, because 6² + 8² = 36 + 64 = 100 = 10².

Front

Given the lengths 13, 80, and 81, does this form a right triangle?

Back

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

Front

Which set of lengths forms a right triangle: 3, 4, 5 or 3, 4, 7?

Back

3, 4, 5 forms a right triangle because 3² + 4² = 9 + 16 = 25 = 5².

Front

Which set of lengths does not form a right triangle: 14, 15, 29 or 38, 80, 90?

Back

14, 15, 29 does not form a right triangle because 14² + 15² = 196 + 225 = 421, which is not equal to 29² (841).

Front

What is a right triangle?

Back

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

Front

What are the side lengths of a right triangle called?

Back

The side lengths of a right triangle are called the legs (a and b) and the hypotenuse (c), which is the longest side opposite the right angle.

Front

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

Back

Yes, because 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.