SOLUTION: Euclid's Proof: the area of the whole square equals the sum of its parts. 1) Write an expression for the area of the large square. Then simplified your expression. 2) write an

Question 203812This question is from textbook Discoverig geometry an investigative approach
:
Euclid's Proof: the area of the whole square equals the sum of its parts.
1) Write an expression for the area of the large square. Then simplified your expression.
2) write an expression for each part of the diagram and sum them up.
triangle 1=?, triangle 2=?, triangle 3=?,triangle 4=?, and the small rectangle=?.
3) Now set your expression for the area of the large square equal to the expression for the sum of the parts and simplify!
PLEASE HELP ME ABOUT THIS. ITS DUE TOMORROW JULY 22ND, PLEASE HELP ME...................This question is from textbook Discovering geometry an investigative approach.
---- .----------------.-!
a ! . . 2 . !
!1 . . . !
!. . !
! . small . !
! . rec . 3 !
b ! 4 . . !
! . . !
------ .----------------
a b
first its a rectangle . it has another rectangle in its body. then it has another small rectangle. i've tried my best to draw it. pls help me...

This question is from textbook Discoverig geometry an investigative approach

Answer by RAY100(1637) (Show Source): You can put this solution on YOUR website!
From "Discovering Geometry, an investigative approach" by M Serra, Key Press, 2003, chpt 9,,pg 463.
,
1) Area of large (a+b)^2, which equals a^2 +2ab+b^2
.
2) All small triangles are, A= (1/2) ab
.
Total area of 4 small triangles is, 4* (1/2) ab = 2ab
.
Small "quadrilateral", A= {a^2 +2ab +b^2} -2ab = a^2 + b^2
.
3)HOWEVER, the small"quadrilateral" is a square, with A=c^2
.
Therefore, c^2 = a^2 +b^2
.
Which is the Pythagorean Theorem.
.
Please see page 463, for more detail

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