Pythagorean Theorem Converse without triangle

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

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

Back

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

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, while the other two sides are called the legs.

Front

If the lengths of the legs of a triangle are 3 and 4, what is the length of the hypotenuse?

Back

The hypotenuse is 5, calculated using the Pythagorean Theorem: 3² + 4² = 9 + 16 = 25, so c = √25 = 5.

Front

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

Back

No, because 15² + 30² = 225 + 900 = 1125, which is not equal to 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 hypotenuse is always the longest side, and the sum of the squares of the legs equals the square of the hypotenuse.

Front

If a triangle has sides of lengths 14, 15, and 29, does it form a right triangle?

Back

No, because 14² + 15² = 196 + 225 = 421, which is not equal to 29² = 841.

Front

What is the formula to find the hypotenuse of a right triangle?

Back

The formula to find the hypotenuse (c) is c = √(a² + b²), where a and b are the lengths of the legs.