15. which of the following figures will not tessellate the plane?
a. rhombus
b. equilateral triangle
c. regular hexagon
d. regular pentagon
Go ahead, try to make a tile floor out of regular pentagon tiles
To determine which figure will not tessellate the plane, we need to understand the concept of tessellation.
Tessellation refers to covering a plane with congruent copies of a shape without any gaps or overlaps. In other words, the shape must fit together perfectly to create a repeating pattern.
Let's analyze each option:
a. Rhombus: A rhombus can tessellate the plane. We can cover the plane with congruent rhombi, aligning them to create a repeating pattern.
b. Equilateral triangle: An equilateral triangle can tessellate the plane. We can cover the plane with congruent equilateral triangles, aligning them to create a repeating pattern.
c. Regular hexagon: A regular hexagon can tessellate the plane. We can cover the plane with congruent regular hexagons, aligning them to create a repeating pattern.
d. Regular pentagon: A regular pentagon cannot tessellate the plane. This is because the interior angles of a regular pentagon measure 108 degrees, and any shape that meets at a vertex of a regular pentagon must have an interior angle that is a divisor of 360 degrees. As 108 degrees is not a divisor of 360 degrees, it is not possible to create a repeating pattern that covers the plane using only regular pentagons.
Therefore, option d. Regular pentagon is the answer. It will not tessellate the plane.
To determine which figure will not tessellate the plane, we need to understand what tessellation is. Tessellation is the process of creating a tiled pattern by fitting together regular, repeated shapes with no gaps or overlaps.
To answer this question, we need to identify a figure that cannot be repeated without gaps or overlaps. Let's analyze each figure:
a. Rhombus: A rhombus is a quadrilateral with all sides of equal length. It can tessellate the plane by creating a pattern of rhombuses without any gaps or overlaps.
b. Equilateral triangle: An equilateral triangle is a triangle with all sides of equal length and angles of 60 degrees. It can tessellate the plane by forming a pattern of equilateral triangles without any gaps or overlaps.
c. Regular hexagon: A regular hexagon has six sides of equal length. It can tessellate the plane by creating a pattern of regular hexagons without any gaps or overlaps.
d. Regular pentagon: A regular pentagon has five sides of equal length. Unfortunately, a regular pentagon does not tessellate the plane. If we try to repeat a regular pentagon, gaps or overlaps will occur, preventing a seamless pattern. Therefore, the regular pentagon is the figure that will not tessellate the plane.
In this case, the correct answer is d. Regular pentagon.