Question

Todd draws a diagram using four identical right triangles to form a square as shown. which best describes how to use the areas of the shaded triangles to begin a proof of the phythagorean theorem?

Answer 1

Answer:

Option (3)

Step-by-step explanation:

From the picture attached,

Area of white square = (side)²

Length of each side of the white square = (b - a)

Area of white square = (b - a)²

Area of each right triangle = $\frac{1}{2}(\text{Base})(\text{Height})$

                                            = $\frac{1}{2}(a)(b)$

Area of four right triangles = Area of big square - Area of white square

                                    = $c^{2}-(b-a)^2$

Since area of 4 right triangles = 4(Area of each right triangle)

c² - (b - a)² = $4[\frac{1}{2}(ab)]$

Therefore, Option (3) will be the answer.