HSA 2007 Algebra/Data Analysis Item 28print

HSA 2007 Algebra/Data Analysis Item 28

CID
CID84dfecc615589a420f420b802a0afa37
itemNum
28
initialLetter
itemType
ECR
itemAnswerKey
N/A
itemMaxScorePoints
4
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x

A triangle, a quadrilateral, a pentagon, and a hexagon are shown below. By drawing a diagonal from 1 vertex, the quadrilateral is divided into 2 non-overlapping triangles. Since the sum of the angle measures of a triangle is 180°, the sum of the measures of the quadrilateral is 360°. By drawing the diagonals from 1 vertex, the pentagon is divided into 3 non-overlapping triangles.

Complete the following in the Answer Book:

  • In the Answer Book, draw the diagonals from 1 vertex of the hexagon so that the hexagon is divided into non-overlapping triangles.
  • Use the polygons above to complete the table in the Answer Book.
    Polygon Number of Sides Number of Non-Overlapping Triangles Sum of Angle Measures
    Triangle 3 1 180°
    Quadrilateral 4 2 360°
    Pentagon 5 3 ?
    Hexagon ? ? ?
  • Describe how the number of sides of each polygon is related to the number of non-overlapping triangles. Use mathematics to justify your answer.
  • Describe how the number of non-overlapping triangles in a polygon is related to the sum of its angle measures. Use mathematics to justify your answer.

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