Exploring the Pythagorean Theorem Proof

The video tutorial explains the Pythagorean theorem using a right triangle with sides of 3 and 4. It demonstrates how to calculate the area of squares drawn on the triangle's legs and shows that the sum of these areas equals the area of the square on the hypotenuse. The tutorial includes a coloring exercise to help visualize the theorem, reinforcing the concept that the area of the squares on the legs equals the area of the square on the hypotenuse.

What is the length of each side of the right triangle mentioned at the beginning?

• 4 and 5

• 2 and 3

• 5 and 6

• 3 and 4

What is the area of the square drawn off the shorter leg of the triangle?

• 25

• 16

• 12

• 9

What is the area of the square drawn off the longer leg of the triangle?

• 12

• 16

• 25

• 9

According to the Pythagorean theorem, what is the sum of the areas of the squares on the two legs?

• 29

• 34

• 25

• 45

What is the length of the hypotenuse in the right triangle?

• 8

• 7

• 5

• 6

How is the area of the square on the hypotenuse related to the areas of the squares on the other two sides?

• It is twice the area of the larger square.

• It is half the sum of the other two areas.

• It is the sum of the other two areas.

• It is the difference between the two areas.

What mathematical operation is used to find the length of the hypotenuse from its area?

• Square root

• Subtraction

• Multiplication

• Division

What is the purpose of coloring the squares in the activity?

• To visually prove the Pythagorean theorem

• To practice coloring skills

• To differentiate between the squares

• To calculate the areas more easily

What does the area of a square drawn off the hypotenuse represent in relation to the other two squares?

• The sum of their areas

• Half the sum of their areas

• Twice the area of the larger square

• The difference of their areas