Exploring the Pythagorean Theorem

In this video, Mr. Jay provides a visual representation of the Pythagorean theorem using a right triangle with side lengths of 4, 3, and 5 feet. He explains how to identify the triangle's sides as a, b, and c, and demonstrates the theorem by squaring these sides to form squares. The video shows that the sum of the areas of the squares on the two shorter sides equals the area of the square on the hypotenuse. Mr. Jay verifies the equation a² + b² = c² with these values, confirming the theorem's validity for all right triangles.

What equation is used in the Pythagorean theorem?

• a^3 + b^3 = c^3

• 2a + 2b = c

• a^2 - b^2 = c^2

• a^2 + b^2 = c^2

Which sides of the triangle are interchangeable in the Pythagorean theorem?

• None, all sides are fixed

• Leg a and hypotenuse c

• Legs a and b

• Leg b and hypotenuse c

What does the hypotenuse represent in a right triangle?

• The longest side

• The shortest side

• Both A and C

• The side opposite the right angle

How do the areas of the squares on the legs compare to the area of the square on the hypotenuse?

• They are more

• They are equal

• They are less

• They add up to the area of the square on the hypotenuse

What is the area of the square on side a if a is 4 feet?

• 12 square feet

• 16 square feet

• 20 square feet

• 8 square feet

What is the sum of the areas of the squares on the legs of the triangle?

• 35 square feet

• 25 square feet

• 20 square feet

• 30 square feet

What proves the Pythagorean theorem in the given example?

• The legs are interchangeable

• The hypotenuse is the longest side

• The sum of the leg areas equals the hypotenuse area

• The triangle has a right angle

What is the correct representation of the Pythagorean theorem with the given side lengths?

• 16 + 9 = 5^2

• 4^2 + 3^2 = 5^2

• 4 + 3 = 5

• 16 + 9 = 25

Is the Pythagorean theorem applicable to all right triangles?

• Yes, without exception

• No, only to triangles with sides 3, 4, 5

• Yes, but only if the hypotenuse is the longest side

• No, it's only a theory

What is the main purpose of the Pythagorean theorem?

• To calculate the perimeter of a triangle

• To prove that a triangle is right

• To find the relationship between the sides of a right triangle

• To calculate the area of a triangle