Exploring Algebraic Proofs of Pythagoras' Theorem

What is the area of the square formed by the hypotenuse in the first algebraic proof?

• b^2

• a^2 + b^2

• a^2

• c^2

In the second algebraic proof, what is the area of the large square?

• a^2 + 2ab + b^2

• 2ab

• a^2 + b^2

• c^2

What geometric shape is formed by dropping a perpendicular from the right angle to the hypotenuse in the third proof?

• A rectangle

• A square

• A trapezium

• Two similar triangles

In the third proof, what is the relationship between the smaller triangles and the original triangle?

• They are congruent

• They are different

• They are similar

• They are identical

Who is credited with the fourth algebraic proof of Pythagoras' theorem?

• Isaac Newton

• Albert Einstein

• James Garfield

• Pythagoras

What geometric shape is used in Garfield's proof?

• A square

• A trapezium

• A triangle

• A circle

In the fifth proof, what is the area of the quadrilateral formed by rotating the triangle?

• a^2

• b^2

• c^2

• 1/2 c^2

What is the result of the equation derived in the sixth proof?

• a^2 + b^2 = c^2

• a^2 - b^2 = c^2

• a^2 + b^2 = 2c^2

• a^2 = b^2 + c^2

In the seventh proof, what is the final equation obtained?

• a^2 + b^2 = 2c^2

• a^2 - b^2 = c^2

• a^2 = b^2 + c^2

• a^2 + b^2 = c^2

What additional resources are mentioned at the end of the video?

• Books

• Online articles

• Geometric proofs video

• Mathematics journals