What must be true for a pentagon so that it will tessellate a plane?
To determine what must be true for a pentagon to tessellate a plane, we first need to understand what tessellation is. Tessellation is the process of filling a plane with repeated copies of a shape, without any gaps or overlaps.
In order for a pentagon to tessellate a plane, the following conditions must be met:
1. Interior Angles: The interior angles of the pentagon must add up to 360 degrees. Since a pentagon has five sides, each interior angle must measure 360/5 = 72 degrees.
2. Equal Side Lengths: All sides of the pentagon must be of equal length. If the sides are not equal, then it will not be possible to create a seamless tessellation.
3. Congruent Angles: The angles of the pentagon must be congruent (meaning they have the same measure). If the angles are not congruent, it will not be possible to fit multiple copies of the shape together.
There are different types of pentagons that satisfy these conditions and can tessellate a plane. One such example is a regular pentagon, where all sides and angles are congruent.
Therefore, to answer your question, a pentagon must have interior angles of 72 degrees, equal side lengths, and congruent angles in order to tessellate a plane.