Write a two column proof. If ZY=3XY, then ZX=4XY
 

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1. ZX=ZY+YX Segment ZX is made up of two adjacent segments ZY and YX
2. ZY=3XY Given
3. YX≡XY Length X→Y is the same as length Y→X, so YX and XY are equivalent

4. ZX=3XY+XY=4XY

QED

Rewrite 1 substituting for ZY and using the equivalence of XY and YX

by Top Rated User (764k points)

At each step we are dealing with the property length. XY, for example, is a segment with a particular unique length. The segment doesn’t even have to be a straight line, but it will always have a fixed length. XY could be the arc of a circle, for instance. So in this proof we are adding lengths together: in geometry we specify the labels at each end of a segment to mean the length of the segment. When we say ZY=3XY we mean the length from a point Z to a point Y (and vice versa: point Y to point Z) is 3 times the length from point X to point Y (and vice versa). 

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