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 is 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 if a² + b² = c², then the triangle is a right triangle.

Front

How can you determine if a set of side lengths forms a right triangle?

Back

To determine if a set of side lengths forms a right triangle, check if the sum of the squares of the two shorter sides equals the square of the longest side.

Front

What are the side lengths of a right triangle?

Back

In a right triangle, the side opposite the right angle is called the hypotenuse, and the other two sides are called the legs.

Front

If the side lengths are 3, 4, and 5, does it form a right triangle?

Back

Yes, because 3² + 4² = 9 + 16 = 25, which equals 5².

Front

If the side lengths are 14, 15, and 29, does it form a right triangle?

Back

No, because 14² + 15² = 196 + 225 = 421, which does not equal 29² (841).

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

Can the lengths 9, 12, and 15 form a right triangle?

Back

Yes, because 9² + 12² = 81 + 144 = 225, which equals 15².

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.