115 Polygons ANSWER: ANSWER: ANSWER:


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1 Determine whether the figure is a polygon. If it is, classify the polygon. If it is not a polygon, explain why KALEIDOSCOPE The kaleidoscope image shown is a regular polygon with 14 sides. What is the measure of one interior angle of the polygon? Round to the nearest tenth. The figure is not a polygon because it is an open figure. Two of the sides are not connected The figure has 8 sides that only intersect at their endpoints. It is an octagon. 6. Determine whether or not an equilateral triangle can be used to make a tessellation. If not, explain. yes 3. Determine whether the figure is a polygon. If it is, classify the polygon. If it is not a polygon, explain why. 7. The figure has 5 sides that only intersect at their endpoints. It is a pentagon. 4. MULTIPLE CHOICE The sum of the measures of the interior angles of a certain regular polygon is How many sides does this polygon have? A 9 sides B 10 sides C 11 sides D 12 sides D 8. The figure has 5 sides that only intersect at their endpoints. It is a pentagon. The figure has 8 sides that only intersect at their endpoints. It is an octagon. esolutions Manual  Powered by Cognero Page 1
2 The figure has 6 sides that only intersect at their endpoints. It is a hexagon. The figure is not a polygon because it has sides that cross each other. The figure has 9 sides that only intersect at their endpoints. It is a nonagon gon gon NATURE The individual cells of a honeycomb are hexagons. What is the measure of an interior angle of a honeycomb? ARCHITECTURE The dome in a state capitol building is octagonal. What is the measure of an interior angle of an octagon? 135 Determine whether or not a tessellation can be created using each regular polygon. If not, explain. 19. quadrilateral yes gon The figure is not a polygon because it has a curved side. Find the sum of the measures of the interior angles of each polygon. 13. decagon gon 1620 no; Each interior angle of a regular 12gon measures 150 and 360 is not evenly divisible by gon no; Each interior angle of a regular 15gon measures 156 and 360 is not evenly divisible by gon no; Each interior angle of a regular 20gon measures 162 and 360 is not evenly divisible by 162. esolutions Manual  Powered by Cognero Page 2
3 Identify the polygon given the sum of the interior angle measures º octagon º 15gon º 20gon º 30gon TESSELLATIONS You can create a tessellation using a translation. a. Draw a square. Then draw a triangle inside the top of the square. b. Translate or slide the triangle from the top to the bottom of the square. c. Repeat this pattern unit to create a tessellation. Use a translation to create a tessellation for each pattern shown ART Refer to the mosaic below. 29. How are tessellations used to create the image? The artist used translations of a square and an octagon to make the tessellating pattern. esolutions Manual  Powered by Cognero Page 3
4 OPEN ENDED Use two types of polygons to create a tessellation that is different from the tessellations shown in this lesson. Describe the polygons and the transformation that you used. Sample answer: When a side of a polygon is extended, an exterior angle is formed. In any polygon, the sum of the measures of the exterior angles, one at each vertex, is 360. Find the measure of an exterior angle of each regular polygon. 31. triangle octagon 45 squares, equilateral triangles; translations, reflections, or rotations 36. REASONING If the number of sides of a regular polygon increases by 1, what happens to the sum of the measures of the interior angles? It increases by ERROR ANALYSIS Jacinta says that it is possible to use a trapezoid to create a tessellation. Robert says this is impossible because the interior angles of a trapezoid are not congruent. Is either of them correct? Explain your reasoning. Jacinta; the interior angles of a polygon do not have to be congruent in order to create a tessellation. The sum of their measures at a vertex must equal decagon gon 24 esolutions Manual  Powered by Cognero Page 4
5 38. CHALLENGE Create a tessellation using regular hexagons and equilateral triangles. 39. WRITING IN MATH Describe the difference between a regular polygon and a polygon that is irregular. Then explain the process used to find the interior angle measure of a regular polygon. Sample answer: A regular polygon has all sides congruent and all angles congruent. A polygon that is not regular has different side lengths, different angle measures, or both. To find the interior angle measure of a regular polygon, subtract 2 from the number of sides, multiply the result by 180, then divide that result by the number of angles. 40. Which term identifies the shaded part of the design shown? 41. The sum of the measures of the interior angles of a polygon is Find the number of sides of the polygon. F 10 G 14 H 16 J 18 G 42. A landscape architect is looking for a brick paver shape that will tessellate. Which shape by itself will allow her to tessellate a patio area? A B C D A heptagon B hexagon C octagon D pentagon B A 43. GRIDDED RESPONSE What is the measure in degrees of an interior angle of a regular polygon with 20 sides? 162 Determine whether each statement is sometimes, always or never true. 44. A square is a rhombus. always esolutions Manual  Powered by Cognero Page 5
6 45. A parallelogram is a rectangle. sometimes 46. A rectangle is a square. sometimes 47. A parallelogram is a quadrilateral. always 48. A figure has vertices A( 3, 2), B( 1, 1), C( 2, 3), and D( 4, 2). Graph the figure and its image after a rotation of 180 around the origin. 50. GARDENING Suppose you plant a square garden with an area of 300 square feet. What is the minimum amount of fencing needed to enclose the garden if the fencing only comes in wholefoot sections? 70 ft of fencing 51. ALGEBRA Solve x Graph the solution on a number line. x 9.6 Find each quotient ( 8) ( 12) 49. Determine whether the triangles shown are congruent. If so, name the corresponding parts and write a congruence statement Simplify each expression. 56. (5 2) yes; M O, L PNO, LNM P, 57. (7 2) esolutions Manual  Powered by Cognero Page 6
7 58. (10 2) (9 2) esolutions Manual  Powered by Cognero Page 7
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