Looking at the drawing below, prove that A'C' is congruent to C'B'.

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Solution:

The solution put forth here is an algebraic means of solving the problem. The Law of Sines and Law of Cosines are used often in this solution.

Let, and .

Thus,

If C'B' = A'C',

then.

Since, and, .

Therefore,

simplifies to .

Now defining each term in this last expression we get,

Thus,

becomes and after simplifying one is left with A'C' = C'B'.

Therefore, A'C' is congruent to C'B'.

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©1998 by Luke Rapley