Question

A polygon with N sides can be constructed to be equianqluar but not equilateral if... _____________

A polygon with N sides can be constructed to be equilateral but not equilangluar if...________
What needs to be true about n for it to be possible??

Answer 1

equilateral polygon is n greater or equal to 5

Answer 2

In a triangle, equal angles also implies equal sides.
But a rectangle has equal angles but the sides are not equal.

Answer 3

ABCDE is a regular pentagon meaning equal angles and equal sides. If I slide the side AE down to A'E', I have preserved the equal angles but increased the lengths of two sides (AB and DE) while decreasing the length of side AE. So this is a pentagon with equal angles but not equal sides. This procedure can be extended to all the other polygons as well.

Answer 4

Therefore, a polygon with N sides can be constructed to be equianqluar but not equilateral if... N > 3

Answer 5

Okay, well thanks for your help!! :) I can just ask my teacher about that second one.

Answer 6

Alright. You are welcome.

Answer 7

For a triangle, if the sides are equal the angles will be equal too. Draw a segment AB of a certain length. Take a compass and set it to the radius of size AB. With A as center draw a circle. All points on the circle are the same distance from A. With B as center draw a circle and all points on this circle are equal distance from point B. These two circles will intersect at two points one above and one below. If you join either of these two points to A and B, it will only form an equilateral triangle. I can't think of a way to make the triangle lengths equal but not the angles.

But in a four-sided figure, the rhombus is an example of all equal sides but not all equal angles. We just draw a square with all sides equal and then tilt the figure to the side preserving equal lengths but changing the angles.

Starting from a five-sided figure of equal sides, we can simply push one of the vertex inside turning a convex polygon into a concave polygon, maintaining equal lengths but not equal angles as shown in the figure where in the regular pentagon ABCDE, A is pushed to A' until BA' = EA' = BA = EA preserving equal sides but not equal lengths and forming the pentagon A'BCDE:
A polygon with N sides can be constructed to be equilateral but not equiangular if N > 3.

Therefore, for both questions the answer seems to be N > 3.

Answer 8

Alright. Ahah, thanks again!