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2. Earlier, you learned that polygon shapes of four or more sides are not rigid. They can be made rigid by adding diagonal braces. a. How could you use this idea of triangulation to find the sum of the measures of the interior angles of a pentagon? Compare your method and angle sum with others. b. Use similar reasoning to find the sum of the measures of the interior angles of a hexagon. Why is it not necessary that the hexagon be a regular hexagon? c. Complete a table like the one below for polygons having up to 9 sides. Examine your table for patterns relating sides, triangles, and angle sums. Number of Sides | Number of Triangles | Sum of Interior Angles 4 | | 5 | 3 | 540 6 | | d. Predict the sum of the measures of the interior angles of a decagon (10 sides). Check your prediction with a sketch. e. Suppose a polygon has n sides. Write a rule that gives the sum of the measures of its interior angles S as a function of the number of its side's n. f. Test your rule for n = 3 (a triangle) and n = 4 (a quadrilateral). g. Why is your function in Part e a linear function? i. What is the slope of the graph of your function? ii. What does the slope mean in terms of the variables? Does the y-intercept make sense? Why or why not? 

          2. Earlier, you learned that polygon shapes of four or more sides are not rigid. They can be made rigid by adding diagonal braces.
a. How could you use this idea of triangulation to find the sum of the measures of the interior angles of a pentagon? Compare your method and angle sum with others.
b. Use similar reasoning to find the sum of the measures of the interior angles of a hexagon. Why is it not necessary that the hexagon be a regular hexagon?
c. Complete a table like the one below for polygons having up to 9 sides. Examine your table for patterns relating sides, triangles, and angle sums.

Number of Sides | Number of Triangles | Sum of Interior Angles
4 | | 
5 | 3 | 540 
6 | | 

d. Predict the sum of the measures of the interior angles of a decagon (10 sides). Check your prediction with a sketch.
e. Suppose a polygon has n sides. Write a rule that gives the sum of the measures of its interior angles S as a function of the number of its side's n.
f. Test your rule for n = 3 (a triangle) and n = 4 (a quadrilateral).
g. Why is your function in Part e a linear function?
i. What is the slope of the graph of your function?
ii. What does the slope mean in terms of the variables? Does the y-intercept make sense? Why or why not?
Show more…
2. Earlier, you learned that polygon shapes of four or more sides are not rigid. They can be made rigid by adding diagonal braces. a. How could you use this idea of triangulation to find the sum of the measures of the interior angles of a pentagon? Compare your method and angle sum with others. b. Use similar reasoning to find the sum of the measures of the interior angles of a hexagon. Why is it not necessary that the hexagon be a regular hexagon? c. Complete a table like the one below for polygons having up to 9 sides. Examine your table for patterns relating sides, triangles, and angle sums. Number of Sides | Number of Triangles | Sum of Interior Angles 4 | | 5 | 3 | 540 6 | | d. Predict the sum of the measures of the interior angles of a decagon (10 sides). Check your prediction with a sketch. e. Suppose a polygon has n sides. Write a rule that gives the sum of the measures of its interior angles S as a function of the number of its side's n. f. Test your rule for n = 3 (a triangle) and n = 4 (a quadrilateral). g. Why is your function in Part e a linear function? i. What is the slope of the graph of your function? ii. What does the slope mean in terms of the variables? Does the y-intercept make sense? Why or why not?

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Geometry A Common Core Curriculum
Geometry A Common Core Curriculum
Ron Larson, Laurie Boswell 1st Edition
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Earlier, you learned that polygon shapes of four or more sides are not rigid. They can be made rigid by adding diagonal braces. a. How could you use this idea of triangulation to find the sum of the measures of the interior angles of a pentagon? Compare your method and angle sum with others. b. Use similar reasoning to find the sum of the measures of the interior angles of a hexagon. Why is it not necessary that the hexagon be a regular hexagon? c. Complete a table like the one below for polygons having up to 9 sides. Examine your table for patterns relating sides, triangles, and angle sums. Number of Sides | Number of Triangles | Sum of Interior Angles 4 | | 5 | 3 | 540 6 | | d. Predict the sum of the measures of the interior angles of a decagon (10 sides). Check your prediction with a sketch. e. Suppose a polygon has n sides. Write a rule that gives the sum of the measures of its interior angles S as a function of the number of its side's n. f. Test your rule for n = 3 (a triangle) and n = 4 (a quadrilateral). g. Why is your function in Part e a linear function? i. What is the slope of the graph of your function? ii. What does the slope mean in terms of the variables? Does the y-intercept make sense? Why or why not?
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Transcript

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00:01 Okay, so here they're wanting us to fill in this chart for a number of triangles inside these polygons and then some of interior angles.
00:09 So if we start with four sides, so something like this, you're drawing a line from the vertex to another vertex.
00:20 You get two triangles in there.
00:24 So two times 180 because each triangle adds up to 180 is 360.
00:34 Then for five, if i choose one vertex and i draw all the triangles possible from that vertex, i get three.
00:46 So three, and then three times 180 is 540...
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