Can we say that all regular polygons are made from congruent isosceles triangles?

Answer 1

Please see below.

From the center of a regular polygon, say with #n# sides, we can join all the vertices and form #n# isosceles triangles. Also observe that this center can also be used to draw a circle circumscribing the polygon, for example, as shown in the figure below

Observe that if center is joined to all the vertices, this forms #n# isosceles triangles and as all sides emanating from center form radius of circumscribing circle, they are equal. Further, the third sides of such triangles too are equal as they form sides of regular polygon.

Hence, we can say that all regular polygons are made from congruent isosceles triangles.

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Answer 2

Ella Armstrong

No, not all regular polygons are made from congruent isosceles triangles. Regular polygons with an even number of sides (such as squares, hexagons, octagons, etc.) can be divided into congruent right triangles, but not necessarily isosceles triangles. However, regular polygons with an odd number of sides (such as equilateral triangles, pentagons, heptagons, etc.) can indeed be divided into congruent isosceles triangles.

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.