crystallynn
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- Jan 16, 2010
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explain why any two regular polygons having the same number of sides are similar? :|
similar tringles HELP
- Thread starter crystallynn
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mmm4444bot
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Are you familiar with the following concepts?
Equiangular
Congruent
Regular polygons with N sides can be broken down into N identical triangles by drawing line segments from the center to each vertex.
When comparing two similar polygons, all of these triangles are congruent.
The central angles remain the same regardless of the side lengths of the triangles (i.e., enlargments or reductions of a regular polygon change only the side lengths; the central angles stay the same). The sides of these triangles increase (or decrease) proportionately from one size to another. So, all of the corresponding angles in these "central" triangles are the same. This means that the triangles in both polygons are ALL similar.
Similar triangles give rise to similar regular polygons, in short.
Equiangular
Congruent
Regular polygons with N sides can be broken down into N identical triangles by drawing line segments from the center to each vertex.
When comparing two similar polygons, all of these triangles are congruent.
The central angles remain the same regardless of the side lengths of the triangles (i.e., enlargments or reductions of a regular polygon change only the side lengths; the central angles stay the same). The sides of these triangles increase (or decrease) proportionately from one size to another. So, all of the corresponding angles in these "central" triangles are the same. This means that the triangles in both polygons are ALL similar.
Similar triangles give rise to similar regular polygons, in short.