There are 2 parallelograms, A and B. They have the same angle measures. Both have 2 sides that measure 6 units. Parallelogram As 2nd set of parallel lines are longer than the 2nd set of parallelogram Bs parallel lines. I need to find out if there is a dilation that maps B to A. From what I can think of, there is no dilation that maps A to B even though I know they are similar because they have the same angle measures. I do not know the length of the other 2 sides for each parallelogram, only that they form angles that have the same measures for both A and B. Is it possible to find a dilation that maps B to A?
2026-03-31 03:35:12.1774928112
Can There Be A Dilation That Maps Parallelogram B to Parallelogram A?
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A similarity transformation is uniquely defined by the images of two distinct points. So if you map the endpoints of the 6 unit edge of $A$ to those of the 6 unit edge of $B$, the two paralleleograms have to be congruent. If, on the other hand, you can map e.g. a 12 unit edge of $A$ onto the 6 unit edge of $B$ and the 6 unit edge of $A$ onto a 3 unit edge of $B$, then you can have a dilation if the angle order agrees with this. So it boils down to this: are the same two angles in the same order incident with the 6 unit edge of each parallelogram?