Question

Kira is using the figure shown to prove the Pythagorean theorem. She starts by writing the

Answer 1

Question:

Kira is using the figure shown to prove the Pythagorean theorem. She starts by writing the

equation  $(a+b)^2 - c^2 = 4(\frac{1}{2}ab )$ because she knows two equal ways to represent the area

of the shaded region. Which best describes the next steps Kira should take to complete her

proof?​

Answer:

The correct option is;

d. Simplify both sides of the equation to get a² + 2·a·b + b² - c² = 2·a·b then subtract 2·a·b and add c² to both sides of the equation

Step-by-step explanation:

Here we have

The area of the larger square = (a + b)²

The area of the middle plain shaded square = c²

∴ Area of the shaded region = (a + b)² - c²

The shaded region consists of for right triangles of base, a and height, b therefore, the area of the shaded region is also the area of the four right triangles = 4 × (1/2 × base × height)

= 4×1/2×a×b = 4(1/2·a·b)

Hence area of the shaded region also = 4(1/2·a·b)

Therefore, (a + b)² - c² = 4(1/2·a·b)

Which is a² + 2·a·b + b² - c² = 4 × 1/2 × a·b = 2·a·b

∴ a² + 2·a·b + b² - c² = 2·a·b

Hence a² + 2·a·b + b² - c² + c² = 2·a·b + c² gives

a² + 2·a·b + b² = 2·a·b + c² gives

Also  a² + 2·a·b + b² - 2·a·b = 2·a·b + c² - 2·a·b gives

a² + b² = c² which is Pythagoras theorem