Proving the Pythagorean Theorem using the Area of a Square and its Pieces

This lesson demonstrates how to prove the Pythagorean theorem using a geometric approach. By constructing a square with four right triangles and a smaller square inside, the video shows how to calculate the areas and simplify the expression to arrive at the theorem: a² + b² = c². The lesson concludes with a recap of the proof process.

What is the Pythagorean theorem used for?

• Finding the relationship between the sides of a right triangle

• Calculating the area of a circle

• Measuring the circumference of a square

• Determining the volume of a cube

How many right triangles are used in the proof setup?

• Two

• Three

• Four

• Five

What is the formula for the area of one of the right triangles in the proof?

• a^2 + b^2

• a * b

• c^2

• 1/2 * a * b

What is the expression for the area of the large square in terms of a and b?

• (a + b)^2

• a^2 + b^2

• 2ab

• c^2

What is the final simplified form of the equation that proves the Pythagorean theorem?

• a^2 = b^2 + c^2

• a^2 + b^2 = c^2

• a^2 + c^2 = b^2

• b^2 + c^2 = a^2