Question

symmetry nected in a line of 9. Explain why only three types of regular polygons tessellate the plane. Choose the correct answer below. O A. In order for a regular polygon to tessellate the plane, its angle bisectors must intersect at 90, angles. OB. In order for a regular polygon to tessellate the plane, Its exterior angle measure must be a divisor of 360 Only three regular polygons have exterior angles that divide 360 Those polygons are the equilateral triangle, regular hexagon, and regular nonagon. Oc. In order for a regular polygon to tessellate the plane, its number of sides must divide 9. Therefore only the equilateral triangle, regular hexagon and regular nonagon can tessellate the plane. OD. In order for a regular polygon to tessellate the plane, its interior angle measure must be a divisor of 360". Only three regular polygons have interior angle measures that divide 360 Those polygons are the equilateral triangle, square, and regular hexagon. 10. Jillian wants to know why a regular pentagon will not tessellate the plane. How do you respond? Choose the correct answer below. O A. Fitting regular pentagons side-by-side results in pentagons sharing three vertices without rotation. The fourth and fifth vertex cannot be shared. O B. A pentagon has no line of symmetry in which create a reflection. Without reflecting, the tessellation cannot be created. O C. A pentagon cannot be used to create a glide rotation because it has only one line of symmetry OD. Each interior angle of a regular pentagon is 108". If one puts three pentagons around a vertex, one gets 324°. What is left over is 36° and cannot be an angle of another pentagon

Answer 1

9) The answer would be Option D

Reaon :-

Only three regular polygons tessellate: equilateral triangles, squares, and regular hexagons.Other polygons cant tessellate because of the angles at the corners of the polygons. In order for a regular polygon to tessellate a plane, an integer number of faces have to be able to meet at a point. For regular polygons, that means that the angle of the corners of the polygon has to divide 360 degrees. In addition, for all convex polygons the sum of the exterior angles have to sum to 360 degrees, and for regular polygons that means the exterior angles have to be equal, and sum to 360 degrees.So only equilateral triangle, squares,regular hexagons can tesselate in a plane .

10) The answer would be Option D

Reason:-

In order for a regular polygon to tessellate , the interior angle of your polygon must divide 360 degrees evenly. Since 108 does not divide 360 evenly, the regular pentagon does not tessellatein the plae .In another approach if you try to fit pentagons at the outer edges of a regular pentagon then each interior angle of pentagon is 108degree. Soo the remaining 252 degree cannot be divided equally so as to make the angle 360degree externally.