Converse of Pythagorean Theorem

Front

What is the Converse of the Pythagorean Theorem?

Back

If in a triangle, the square of the length of one side is equal to the sum of the squares of the lengths of the other two sides, then the triangle is a right triangle.

Front

What is a right triangle?

Back

A triangle that has one angle measuring 90 degrees.

Front

If a triangle has sides of lengths 3, 4, and 5, is it a right triangle?

Back

Yes, because 3² + 4² = 5² (9 + 16 = 25).

Front

What is the formula for the Pythagorean Theorem?

Back

a² + b² = c², where c is the length of the hypotenuse.

Front

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

Back

Check if the square of the longest side equals the sum of the squares of the other two sides.

Front

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

Back

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

Front

What does it mean if a triangle does not satisfy the Pythagorean Theorem?

Back

It means the triangle is not 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 = 13² (25 + 144 = 169).

Front

What is the relationship between the sides of a right triangle?

Back

The square of the hypotenuse is equal to the sum of the squares of the other two sides.

Front

If a triangle has sides of lengths 7, 24, and 25, is it a right triangle?

Back

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