Question

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
( i get confused at the (a-b)^2 )

Answer 1

(a-b)^2 + (4 a b/2)

= a^2 - 2 a b + b^2 + 2 a b

= a^2 + b^2

but as you know
c^2 = a^2 + b^2
is the Pythagorean Theorem

Answer 2

Look at this
scroll down to "algebraic proofs"
http://en.wikipedia.org/wiki/Pythagorean_theorem

Answer 3

THANKS AGAIN