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Why do equilateral triangles tessellate?

Answer 1

A shape will tessellate if its vertices can have a sum of #360˚#.

In an equilateral triangle, each vertex is #60˚#. Thus, #6# triangles can come together at every point because #6xx60˚=360˚#.

This also explains why squares and hexagons tessellate, but other polygons like pentagons won't.

A square will form corners where #4# squares meet, since #4xx90˚=360˚#.

Similarly, a regular hexagon has an angle measure of #120˚#, so #3# regular hexagons will meet at a point in a hexagonal tessellation since #3xx120˚=360˚#.

A pentagon, however, has an internal angle measure of #108˚#, which isn't a nice factor of #360˚#.

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Answer 2

Parker Allen

Equilateral triangles tessellate because the angles of an equilateral triangle are all 60 degrees, and the sum of angles around any vertex in a tessellation must equal 360 degrees. Since 360 divided by 60 equals 6, exactly six equilateral triangles can meet at each vertex without leaving any gaps or overlaps. This property allows equilateral triangles to fit together perfectly without leaving any space, making them suitable for tessellation.

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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.