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: c² = a² + b².

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

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 are the side lengths of a right triangle?

Back

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

Front

How can you determine if a triangle is a right triangle using side lengths?

Back

You can use the Converse of the Pythagorean Theorem: check if a² + b² = c², where c is the longest side.

Front

Given sides 8, 15, and 17, is this a right triangle?

Back

Yes, because 8² + 15² = 64 + 225 = 289 = 17².

Front

What is the hypotenuse in a right triangle?

Back

The hypotenuse is the side opposite the right angle and is the longest side of the triangle.

Front

Can the sides 7, 24, and 25 form a right triangle?

Back

Yes, because 7² + 24² = 49 + 576 = 625 = 25².

Front

If a triangle has sides 9, 12, and 15, is it a right triangle?

Back

No, because 9² + 12² = 81 + 144 = 225, which is not equal to 15².

Front

What is the formula to find the length of the hypotenuse?

Back

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