One way I suppose you could do it is by saying the opposite, and then try to prove yourself wrong:eckiller said:I have the transformation:
z' = g(z) = f*z / (f-n) - f*n / (f-n)
f >= 0 , n>= 0 constants that define an interval [n, f].
I want to prove, z' <= z.
A transformation proof is a mathematical technique used to prove that two geometric figures are congruent. It involves applying a series of transformational steps, such as translations, rotations, reflections, and dilations, to one figure in order to transform it into the other figure.
The transformations used in a proof depend on the specific problem and the given information. Generally, it is helpful to start with the most obvious transformation, such as a translation or rotation, and then consider other possibilities. It may also be helpful to draw a diagram or use manipulatives to visualize the problem.
The purpose of a transformation proof is to provide a logical and visual justification for the congruence of two figures. It allows us to use properties of transformations, which are easier to understand and work with, to prove properties of geometric figures.
Some common mistakes to avoid in a transformation proof include not following the given information, using incorrect or incomplete transformations, and not fully justifying each step of the proof. It is also important to be careful with labeling and notation, as mistakes in these areas can lead to incorrect conclusions.
One helpful tip for completing a transformation proof is to work backwards from the desired result. This means starting with the final figure and thinking about what transformations would need to be applied to get to that figure. It can also be helpful to look for symmetry or other patterns in the figures that may make the proof easier to complete.