2.4 Angle Properties in Polygons.notebook. October 27, 2013 ENTRANCE SLIP

Transcription

1 ENTRANCE SLIP If you are given one interior angle and one exterior angle of a triangle, can you always determine the other interior angles of the triangle? Explain, using diagrams. 1

2 2.4 Angle Properties in Polygons EXPLORE... A pentagon has three right angles and four sides of equal length, as shown. What is the sum of the measures of the angles in the pentagon? SAMPLE ANSWER 2

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4 Angle Properties in Polygons Polygon # of sides # of triangles Sum of Angle Measures triangle quadrilateral 4 pentagon 5 hexagon 6 heptagon 7 octagon 8 Draw the polygons listed in the table above. Create triangles to help you determine the sum of the measures of their interior angles. Record your results in a table like the one above. Make a conjecture about the relationship between the sum of the measures of the interior angles of a polygon, S, and the number of sides of the polygon, n. Use your conjecture to predict the sum of the measures of the interior angles of a dodecagon (12 sides). Verify your prediction using triangles. 4

5 Polygon # of sides # of triangles Sum of Angle Measures triangle 3 # of triangles 180 quadrilateral 4 pentagon 5 hexagon 6 heptagon 7 octagon 8 Draw the polygons listed in the table above. Create triangles to help you determine the sum of the measures of their interior angles. Record your results in a table like the one above. Make a conjecture about the relationship between the sum of the measures of the interior angles of a polygon, S, and the number of sides of the polygon, n. Use your conjecture to predict the sum of the measures of the interior angles of a dodecagon (12 sides). Verify your prediction using triangles. 5

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7 Part Two Exterior Angles Properties Sum of Exterior Angles of Polygons Draw a rectangle. Extend each side of the rectangle so that the rectangle has one exterior angle for each interior angle. Determine the sum of the measures of the exterior angles. What do you notice about the sum of the measures of each exterior angle of your rectangle and its adjacent interior angle? Would this relationship also hold true for the exterior and interior angles of the irregular quadrilateral shown? Explain. Make a conjecture about the sum of the measures of the exterior angles of any quadrilateral. Test your conjecture. Draw a pentagon. Extend each side of the pentagon so that the pentagon has one exterior angle for each interior angle. Based on your diagram, revise your conjecture to include pentagons. Test your revised conjecture. Do you think your revised conjecture will hold for polygons that have more than five sides? Explain and verify by testing. 7

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9 In your notes Copy the definition of Convex polygon on page 96. Also copy the chart In Summary on page 99 9

10 Angle Properties in Polygons 10

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21 Practice Problems on pages in text. # 2, 3, 6, 7A,7B, 10, 16, and 20 21

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23 Pull for Lesson Notes Answers 23

24 Attachments PM11 2s4 interior.gsp PM11 2s4 exterior.gsp 2s4e1 finalt.mp4 2s4e2 finalt.mp4 2s4e3 finalt.mp4