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ryanbasdao
07.09.2020 •
Mathematics
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?
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Ответ:
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})](/tpl/images/0744/5787/7363f.png)
=![\frac{1}{2}(a)(b)](/tpl/images/0744/5787/e22f3.png)
Area of four right triangles = Area of big square - Area of white square
=![c^{2}-(b-a)^2](/tpl/images/0744/5787/37783.png)
Since area of 4 right triangles = 4(Area of each right triangle)
c² - (b - a)² =![4[\frac{1}{2}(ab)]](/tpl/images/0744/5787/26125.png)
Therefore, Option (3) will be the answer.
Ответ: