Understanding the Converse of the Pythagorean Theorem

This video tutorial reviews the converse of the Pythagorean theorem, which states that if a triangle is a right triangle, then the sum of the squares of the two shorter sides equals the square of the longest side. The video provides examples to determine if given side lengths form a right triangle. The first example confirms that the sides 5, 12, and 13 form a right triangle, while the second example shows that the sides 7, 8, and 15 do not form a right triangle, as they do not satisfy the Pythagorean theorem.

What does the converse of the Pythagorean theorem state?

• If a squared plus b squared equals c squared, then the triangle is a right triangle.

• If a triangle is isosceles, then a squared plus b squared equals c squared.

• If a triangle is a right triangle, then a squared plus b squared equals c squared.

• If a triangle is equilateral, then a squared plus b squared equals c squared.

In the example with sides 5, 12, and 13, which side is considered the hypotenuse?

• 13

• None of these

• 12

• 5

What is the result of 5 squared plus 12 squared?

• 113

• 25

• 169

• 144

Why can we conclude that the triangle with sides 5, 12, and 13 is a right triangle?

• Because 5 squared minus 12 squared equals 13 squared.

• Because 5 times 12 equals 13.

• Because 5 plus 12 equals 13.

• Because 5 squared plus 12 squared equals 13 squared.

What is the largest side in the triangle with sides 7, 8, and 15?

• 15

• 8

• 7

• None of these

What is the sum of 7 squared and 8 squared?

• 49

• 225

• 113

• 64

Does the sum of 7 squared and 8 squared equal 15 squared?

• Only if the triangle is equilateral

• Only if the triangle is right-angled

• No

• Yes

Why do the sides 7, 8, and 15 not form a triangle?

• Because the sum of the two smaller sides is equal to the third side.

• Because the sum of the two smaller sides is not greater than the third side.

• Because the sum of the two smaller sides is greater than the third side.

• Because the sum of the two smaller sides is less than the third side.

What theorem is briefly mentioned in the conclusion about the sides 7, 8, and 15?

• Triangle inequality theorem

• Equilateral triangle theorem

• Pythagorean theorem

• Converse theorem

What is the main focus of the video tutorial?

• Studying the properties of isosceles triangles

• Learning about equilateral triangles

• Exploring the triangle inequality theorem

• Understanding the converse of the Pythagorean theorem