Using the Converse of the Pythagorean Theorem

The video tutorial explains the converse of the Pythagorean theorem, which states that if the square of the longest side of a triangle equals the sum of the squares of the other two sides, the triangle is a right triangle. The teacher sets up a problem involving a right triangle with missing side lengths and guides students through solving it using the theorem. The solution process involves identifying the hypotenuse and calculating the missing side lengths. The video concludes with a verification of the solution and a summary of the key concepts.

What does the converse of the Pythagorean theorem state about a triangle?

• If the sum of the squares of two sides equals the square of the third side, the triangle is a right triangle.

• The sum of the angles in a triangle is 180 degrees.

• The longest side of a triangle is always opposite the largest angle.

• A triangle with equal sides is an equilateral triangle.

In the problem setup, which values were considered as potential hypotenuse candidates?

• 2, 6, and 8

• 8, 10, and 14

• 4, 8, and 16

• 6, 10, and 12

What is the result when you square the number 6?

• 42

• 36

• 18

• 12

After eliminating 8 as a hypotenuse, what was the next value tried?

• 12

• 16

• 10

• 14

What are the final side lengths identified for the right triangle?

• 6, 8, and 10

• 5, 12, and 13

• 7, 24, and 25

• 9, 12, and 15