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 is expressed as a² + b² = c².

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

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

Back

To determine if a triangle is a right triangle, check if the square of the longest side (hypotenuse) is equal to the sum of the squares of the other two sides.

Front

Given the lengths 6, 8, and 10, does this form a right triangle?

Back

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

Front

What lengths form a right triangle?

Back

Lengths that satisfy the Pythagorean Theorem (a² + b² = c²) form a right triangle.

Front

What is the significance of the longest side in a triangle when applying the Pythagorean Theorem?

Back

The longest side is considered the hypotenuse, and it must be opposite the right angle in a right triangle.

Front

Can the Pythagorean Theorem be applied to non-right triangles?

Back

No, the Pythagorean Theorem only applies to right triangles.

Front

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

Back

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

Front

What is the formula to find the hypotenuse of a right triangle?

Back

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

Front

What is a right triangle?

Back

A right triangle is a triangle that has one angle measuring 90 degrees.