Pythagorean 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 is expressed as a² + b² = c².

Front

What is the formula to determine if a triangle is a right triangle using the Pythagorean Theorem?

Back

To determine if a triangle is a right triangle, check if a² + b² = c², where c is the longest side.

Front

What is the longest side of a right triangle called?

Back

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

Front

What type of triangle is formed when all angles are less than 90 degrees?

Back

A triangle with all angles less than 90 degrees is called an acute triangle.

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, which equals 13².

Front

What is the converse of the Pythagorean Theorem?

Back

The converse of the Pythagorean Theorem states that if a² + b² = c², then the triangle with sides a, b, and c is a right triangle.

Front

How can you determine if a triangle is acute using the Pythagorean Theorem?

Back

A triangle is acute if a² + b² > c², where c is the longest side.

Front

How can you determine if a triangle is obtuse using the Pythagorean Theorem?

Back

A triangle is obtuse if a² + b² < c², where c is the longest side.

Front

What are the conditions for three lengths to form a triangle?

Back

The sum of the lengths of any two sides must be greater than the length of the third side.

Front

If a triangle has sides of lengths 8, 15, and 17, what type of triangle is it?

Back

It is a right triangle because 8² + 15² = 64 + 225 = 289, which equals 17².