A line segment is sometimes/never/always similar to another line segment, because we can sometimes/never/always map one onto the other using only dilations and rigid transformations.

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05-04-2020
Mathematics

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A line segment is sometimes/never/always similar to another line segment, because we can sometimes/never/always map one onto the other using only dilations and rigid transformations.

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jimthompson5910 jimthompson5910 · Answer 1 · 2020-04-05T04:08:15+02:00

Answer: "always" for both

A line segment is always similar to another line segment, because we can always map one onto the other using only dilations and rigid transformations.

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Explanation:

A dilation is where we grow or shrink an object. In this case, it would be lengthening or shortening a line. We can dilate any line to get it to any desired length we want. Then to make sure it matches up perfectly with the other line, we can perform translations (aka shifting) and rotations.

In other words, if we have four points A,B,C,D then it is possible to use dilations and rigid transformations to map points A,B to points C,D. The first segment AB would map to segment CD.

codiepienagoya codiepienagoya · Answer 2 · 2021-11-12T19:03:08+01:00

The dilatation is indeed a group of Non-Transformation that alters the structure of our original object. It can, for example, scale our object to make it larger. Able to produce sufficient by dilatation are comparable.

This would be the elongation or shortening of such a line in this example. We can dilate any line to any length we wish.
The stiff conversion does not modify either size or shape of the figure while preserving distance and angles.
Rigid transformations include reflections, translates, rotation, and mixtures of the three.
They can utilize dilatation and rigid transforms to map graph XY to line segment WZ if we have two line segments XY and WZ.
The very first section XY correlates to the second segment WZ.

so "A line is always comparable to some other reference line since they can be mapped into each other using only dilatation and rigid rotations".

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