6-2 Converse of Pythagorean Theorem

Front

What is the Converse of the Pythagorean Theorem?

Back

If a triangle has side lengths a, b, and c, and a^2 + b^2 = c^2, then the triangle is a right triangle.

Front

How do you identify the hypotenuse in a right triangle?

Back

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

Front

What are Pythagorean Triples?

Back

Pythagorean Triples are sets of three positive integers a, b, and c that satisfy the equation a^2 + b^2 = c^2.

Front

Give an example of a Pythagorean Triple.

Back

(3, 4, 5) is a classic example of a Pythagorean Triple.

Front

What is the formula to check if three sides form a right triangle?

Back

To check if sides a, b, and c form a right triangle, verify if a^2 + b^2 = c^2, where c is the longest side.

Front

Can the sides 12, 20, and 16 form a right triangle?

Back

Yes, because 12^2 + 16^2 = 144 + 256 = 400 = 20^2.

Front

What is the significance of the Pythagorean Theorem in geometry?

Back

The Pythagorean Theorem is used to determine the relationship between the sides of a right triangle and is fundamental in geometry.

Front

What is the relationship between the sides of a right triangle and the Converse of the Pythagorean Theorem?

Back

The Converse states that if the square of the longest side equals the sum of the squares of the other two sides, the triangle is a right triangle.

Front

How can you determine if a set of numbers is a Pythagorean Triple?

Back

Square each number, and check if the sum of the squares of the two smaller numbers equals the square of the largest number.

Front

What is the result of checking the sides 18, 73, and 75 for being a Pythagorean Triple?

Back

No, because 18^2 + 73^2 = 324 + 5329 = 5653, which does not equal 75^2 (5625).