which shape will create tessellation using
only translations?
A. scalene triangle
B. regular hexagon
C. equilateral triangle
D. isosceles trapezoid
C.Equilateral triangle
The shape that will create tessellation using only translations is the regular hexagon (B).
To determine which shape will create a tessellation using only translations, we need to consider the properties of tessellations.
A tessellation is a repeating pattern of shapes that completely covers a plane without any gaps or overlaps. In order for a shape to tessellate using only translations, it must be able to slide (translate) without rotating or reflecting.
Let's analyze each option:
A. Scalene Triangle: A scalene triangle is a triangle with unequal side lengths and angles. It is not possible for a scalene triangle to tessellate using only translations because the angles of a scalene triangle are different, and therefore, they cannot fit together without rotating or reflecting.
B. Regular Hexagon: A regular hexagon is a six-sided polygon with equal sides and angles. A regular hexagon can tessellate the plane using only translations. By sliding (translating) copies of the hexagon, all the sides can perfectly fit together without any gaps or overlaps.
C. Equilateral Triangle: An equilateral triangle is a triangle with three equal sides and angles measuring 60 degrees each. It is not possible for an equilateral triangle to tessellate using only translations because the angles of an equilateral triangle cannot fit together without rotating or reflecting.
D. Isosceles Trapezoid: An isosceles trapezoid is a four-sided polygon with two parallel sides and two non-parallel sides. It is not possible for an isosceles trapezoid to tessellate using only translations because the angles of an isosceles trapezoid are not the same, and therefore, they cannot fit together without rotating or reflecting.
Based on the analysis, the shape that will create a tessellation using only translations is B. Regular hexagon.