Will a non-regular acute triangle tessellate the plane?
No, a non-regular acute triangle will not tessellate the plane. In order for a shape to tessellate the plane, it must be able to cover an infinite plane without any gaps or overlaps.
To determine if a triangle can tessellate the plane, we can apply a simple rule: the sum of the angles in a triangle must be 180 degrees. For an equilateral triangle (a regular triangle with all angles equal), each angle is 60 degrees, and since 60 + 60 + 60 = 180, it satisfies the requirement for tessellation.
However, in the case of a non-regular acute triangle, it has one angle larger than 90 degrees and two smaller angles. Let's assume that one angle is larger than 90 degrees, say 100 degrees. Now, the sum of the remaining two angles must be less than 80 degrees (180 - 100 = 80). Since the smallest angle that can be formed in a triangle is 0 degrees, it means that the sum of the remaining two angles cannot fulfill the requirement of 80 degrees. Therefore, a non-regular acute triangle cannot tessellate the plane.
To summarize, a non-regular acute triangle cannot tessellate the plane because its angles cannot add up to 180 degrees, which is a necessary condition for tessellation.