Converse of Pythagorean Theorem 9.5.1

Front

What is the Converse of the Pythagorean Theorem?

Back

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

Front

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

Back

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

Front

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

Back

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

Front

Given the sides 8, 15, and 17, determine if it forms a right triangle.

Back

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

Front

What are the side lengths of a right triangle if one side is 6 and the other is 8?

Back

The hypotenuse is 10, because 10² = 6² + 8² (100 = 36 + 64).

Front

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

Back

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

Front

What does it mean if the Pythagorean Theorem does not hold true for a triangle?

Back

It means the triangle is not a right triangle.

Front

For the sides 5, 12, and 13, verify if it is a right triangle.

Back

Yes, because 13² = 5² + 12² (169 = 25 + 144).

Front

What is the significance of the longest side in the Pythagorean Theorem?

Back

The longest side is always the hypotenuse in a right triangle.

Front

If a triangle has sides of lengths 9, 12, and 15, does it form a right triangle?

Back

No, because 15² ≠ 9² + 12² (225 ≠ 81 + 144).