Pythagoras Theorem and its 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 a right triangle?

Back

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

Front

What is the longest side of a right triangle called?

Back

The longest side of a right triangle is called the hypotenuse.

Front

Can side lengths 6, 8, and 10 form a right triangle?

Back

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

Front

True or False: To determine if 3 side lengths form a right triangle, add the areas of the squares on the legs to determine if the sum equals the area of the square on the hypotenuse.

Back

True.

Front

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

Back

The formula is c = √(a² + b²), where c is the hypotenuse and a and b are the other two sides.

Front

If one leg of a right triangle is 3 and the other leg is 4, what is the length of the hypotenuse?

Back

The hypotenuse is 5, because 3² + 4² = 5² (9 + 16 = 25).

Front

True or False: When determining whether or not 3 side lengths form a right triangle, add the side lengths of the legs to see if the sum is equal to the length of the hypotenuse.

Back

False.

Front

What is the converse of the Pythagorean Theorem?

Back

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

Front

What is a leg in a right triangle?

Back

A leg is one of the two shorter sides of a right triangle that form the right angle.