## Find the values of the opposite sides

Geometric formulae, word problems, theorems and proofs, etc.
Bruce
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### Find the values of the opposite sides

Hello Everyone, I have to solve this quadrilateral problem and no idea where or how to start
top left corner is A
bottom left corner is B
bottom right corner is C
top right corner is D

Find a way to get the values of CD and DA
AB - BC = DA - CD
AB - CD = DA - BC
AB + DA = BC + CD

Posts: 136
Joined: Sun Feb 22, 2009 11:12 pm

### Re: Find the values of the opposite sides

Hello Everyone, I have to solve this quadrilateral problem and no idea where or how to start
top left corner is A
bottom left corner is B
bottom right corner is C
top right corner is D

Find a way to get the values of CD and DA
AB - BC = DA - CD
AB - CD = DA - BC
AB + DA = BC + CD
I'd start by naming the lengths: AB = w, BC = x, CD = y, DA = z. Then the equations are:

w - x = z - y
w - y = z - x
w + z = x + y

This is 3 equations in 4 variables which usually isn't solvable. You can get them to standard form for linear systems:

w - x + y - z = 0
w + x - y - z = 0
w - x - y + z = 0

Solving gives:

w = z
x = z
y = z

But there's no way to find z. Sorry.