WORKBOOK SAMPLER Chapter 7: Polygons - Nelson Education

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7.4 Regular Polygons Try These You will need • 6 toothpicks • a ruler • a protractor • a compass Use six toothpicks. Create an irregular hexagon. How do you know that your hexagon is not regular Use a diagram to explain. e.g., The interior angles are not equal. e.g., irregular Pavithra uses regular polygons to make wooden trays. Which regular polygons are in this tray 1 Find a triangle in this tray. Is it a regular polygon Explain. No. e.g., Only two sides are equal. 2 Name all the regular polygons in this tray. square, octagon, pentagon, and hexagon similar polygons polygons that are congruent, or enlargements or reductions of each other; the ratios of corresponding sides are equal and the corresponding angles are equal Example 1 Olivia designs and sells cloth potholders. To make the design at the right, she sewed a light-coloured hexagon on a dark-coloured hexagon. The dark hexagon is slightly larger. The light hexagon is a smaller similar polygon. AW12SB 0176519637 How can Olivia use FN a tracing of C07-F62-AW12SB the dark hexagon to make a model of CO the light hexagon CrowleArt Group Technical Pass 2nd pass Solution Approved A. Mark the midpoint Not Approved of each side. Draw straight lines to join each midpoint to the next midpoint. B. How do you know the shapes are similar e.g., The original shape has six equal sides and equal interior 1208 angles. The new shape also has these properties, but its side lengths are smaller. 174 Apprenticeship and Workplace 12 NEL 18 Apprenticeship and Workplace 12 NEL
C. Test these regular polygons. Does the midpoint reducing method always work to make a similar smaller polygon ReflecTinG Gabriel drew a square. He says that all squares are similar to the square he drew. Do you agree Explain. yes yes yes D. Will all regular polygons have this property Explain. • Joining the midpoints of each side of a regular polygon creates a similar regular polygon. Yes. e.g., The number of midpoints matches the number of vertices, so the polygons are the same type. The distance between the midpoints does not change, so both polygons C07-F65-AW12.ai C07-F67-AW12.ai C07-F66-AW12.ai have equal sides. The angle from one midpoint to the next does not change, so both polygons have equal angles. Example 2 Craig designs and makes signs in Regina. A customer wants a sign that is a regular pentagon. How can Craig determine the angle measures for the sign AW12 0176519637 -F65-AW12.ai Figure Number S Company Technical pass Pass Approved Not Approved Solution A. Sketch a convex pentagon. It can be regular or irregular. AW12 0176519637 Figure Number C07-F66-AW12.ai Company MPS Technical Pass 1st pass (1808) 5 Approved Not Approved B. Draw diagonals from one vertex to divide your pentagon into triangles. How many triangles did you make three C07-F67-AW12.ai MPS C. What is the sum of all the interior angles of your pentagon 1st pass 3 5408 The sum is 5408 . D. What angle measure should Craig use 5408 4 5 5 1088 Craig should use 1088 . A. e.g., ReflecTinG Can you always divide a shape into triangles to determine its angle measures Is this a property of regular polygons Explain. NEL NEL C07-F68-AW12.ai Chapter 7 Polygons 175 Chapter 7 Polygons 19
Page 1 and 2: WORKBOOK SAMPLER Chapter 7: Polygon
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Page 7 and 8: Polygons 7 Zahra is a beekeeper nea
Page 9 and 10: 5. Which triangles in Question 3 ma
Page 11 and 12: C. Is nABM congruent to nCBM How do
Page 13 and 14: 4. Use the angle measures to calcul
Page 15 and 16: Example 1 Elena is a pastry chef in
Page 17 and 18: 5. Jay makes picture frames. The in
Page 19: Mid-chapter 1. Ty says that if you
Page 23 and 24: AW12SB 4. Draw all the diagonals in
Page 25 and 26: Solution A. Use a compass to constr
Page 27 and 28: chapter 1. Circle the polygons. 2.
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WORKBOOK SAMPLER Chapter 7: Polygons - Nelson Education

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