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Is this phrase safe to consider in general:

Equal sides of a polygon have corresponding equal angles

if not how would you refine or correct it

Example of a corresponding angle would be

enter image description here

Edited: For example suppose you ignore the fact that the above triangle is an equilateral and treat it as a regular polygon.Then according to the above statement Angle A and Angle B are both equal because Side A corresponds to angle A which is equal to SideB which corresponds to angle B

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So does this mean that all the angles of a rhombus will be equal ? –  Rajeshwar Jun 10 '12 at 13:42
    
how do you define a corresponding angle in a polygon? –  Valentin Jun 10 '12 at 13:42
    
Just clarified my question a bit more –  Rajeshwar Jun 10 '12 at 13:51
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how would you define corresponding angle for polygon of 4 or more sides?? –  Santosh Linkha Jun 10 '12 at 13:56
    
@experimentX Nice question.. I guess then this statement only applies to triangles what do u think ?.. –  Rajeshwar Jun 10 '12 at 14:01

2 Answers 2

up vote 2 down vote accepted

Construct a pentagon of all equal sides. Physically, out of pieces of straws or something. Note how you can bend it in any which way so that no angles are the same. So the question of "equal sides correspond to equal angles" is true for triangles, can maybe be rephrased in a way that's true for quadrilaterals (since there it forces two pairs of equal angles), but definitely fails to work in general.

A better statement to prove might be the reverse: Do equal angles of a polygon imply equal sides?

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Yeah concluding it I believe this statement only holds for Triangles. I am also interested in the answer to Do equal angles of a polygon imply equal sides? but then experimentX asked a very good question which angles represent which side ? –  Rajeshwar Jun 10 '12 at 14:12
    
@Rajeshwar: if you become interested in a different question from your original question, feel free to ask a new one; if you change this one then the answers will look wrong –  Ben Millwood Jun 10 '12 at 14:12
    
benmachine Ill ask a new one then.. thanks for pointing it out –  Rajeshwar Jun 10 '12 at 14:13

There is a statement about equal triangles that says: in equal triangles the angles opposite to equal sides are equal, i.e. is $\Delta ABC$ = $\Delta A_1B_1C_1$, then $AB=A_1B_1\implies \angle C =\angle C_1$. If you want to generalise this in any direction, you must say something about the polygons in question and the way how angles "correspond" to sides, otherwise the picture is too loose to make a definite statement

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Is this statement only limited to equilateral triangles or could it be applied to other types of triangles as well ? –  Rajeshwar Jun 10 '12 at 14:10
    
it applies to any two or more equal triangles –  Valentin Jun 10 '12 at 14:19
    
you mean any kind of a triangle –  Rajeshwar Jun 10 '12 at 14:22
    
yes, to any kind –  Valentin Jun 10 '12 at 14:31

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