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

How can you determine if three lengths can form a right triangle?

Back

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

Front

Given the lengths 6 cm, 8 cm, and 10 cm, do they form a right triangle?

Back

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

Front

What is the hypotenuse in a right triangle?

Back

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

Front

If the sides of a triangle are 9, 40, and 41, which is the hypotenuse?

Back

41 is the hypotenuse.

Front

Do the sides 9, 12, and 15 form a right triangle?

Back

Yes, because 9² + 12² = 15² (81 + 144 = 225).

Front

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

Back

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

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 does it mean if the sum of the squares of the two shorter sides does not equal the square of the longest side?

Back

It means the triangle is not a right triangle.

Front

Can a triangle with sides 7, 24, and 25 be a right triangle?

Back

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