Andre drew four congruent triangles, with legs a and b units long and hypotenuse c units long. Then, Andre arranged the triangles to form a large square. He then wrote two different expressions for the are of the large square. Since each side measures c, he represented the area as c^2. The area of the large square is also equal to the area of the square hole, (a-b)^2, plus the area of the 4 triangles, (4* ab/2). Then he set the two expressions equal. Simplify the equation c^2 = (a-b)^2 + (4 * ab/2). SHOW ALL WORK AND EXPLAIN PLZ THEN IDENTIFY THE THEOREM IT PROVES PLZ EXPLAIN
so, where do you get stuck?
Hint: 4 * ab/2 = 2ab
the whole thing confuses me honestly
(a-b)^2 confuses me
To simplify the equation c^2 = (a-b)^2 + (4 * ab/2), let's start by simplifying each term step by step:
1. Expand (a-b)^2:
(a-b)^2 = (a-b)(a-b) = a(a-b) - b(a-b) = a^2 - ab - ab + b^2 = a^2 - 2ab + b^2
2. Simplify (4 * ab/2):
(4 * ab/2) = 2ab
Now, substitute these simplified expressions back into the equation:
c^2 = (a-b)^2 + (4 * ab/2)
c^2 = a^2 - 2ab + b^2 + 2ab
Next, combine like terms:
c^2 = a^2 - 2ab + 2ab + b^2
Simplify further:
c^2 = a^2 + b^2
Therefore, the simplified equation is c^2 = a^2 + b^2, which is known as the Pythagorean theorem. This theorem states that in a right triangle, the square of the length of the hypotenuse (c) is equal to the sum of the squares of the lengths of the other two sides (a and b).