Geometer Sketch Pad Assignment

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Geometer Sketch Pad Assignment

• Mark Breakdown

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Exercise 1 Question 1

• Medians
• All three meet at one point
• Circle with a center at the centroid has no
  special properties.
• Bisectors
• All three meet at one point
• Circle with a center at the incenter will touch
  all three sides of the triangle.

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• Altitudes
• All three meet at one point.
• Circle with a center at the orthocenter has no
  special properties.
• Perpendicular Bisectors
• All three meet at one point.
• Circle with a center at the circumcenter will
  touch all three vertices of the triangle.
• 2 marks each total of 8

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Exercise 1 Question 2

• Line AB
• Plot points (3, 4) and (7, -2)
• Construct segment, and construct midpoint (5, 1)
• Line CD
• Plot points (-3, -1) and (2, -9)
• Construct segment, and construct midpoint (-0.5,
  -5)
• Calculate the lengths of each half of the line
  segments to prove they are the same!!
• 2 marks each 4 marks total

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Exercise 1 Question 3

• Plot points!!
• Triangle ABC is right angled and scalene!
• Triangle DFG is right angled and scalene!
• Triangle HIJ is right angles and isosceles!
• Right angled (1 mark each)
• Triangle Type Identified (1 mark each)
• Proof with measurements (1 mark each)
• Total 9 marks

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Exercise 1 Question 4

• Drawing the triangle and making the
  midsegments.(1 mark)
• Calculate Areas outside triangle, inside
  triangle (1 mark)
• Calculate Slopes (1 mark)
• Calculate lengths of lines, and determine ratio
  (1 mark)
• Conclusions (2 marks)
• The lengths of DEF (inside) are exactly half of
  ABC (outside)
• The area of the ABC is exactly 4 times larger
  than DEF (inside)
• The slopes are the same!

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Exercise 2 Question 1

• Construct parallelogram (1 mark)
• Proof that you constructed a parallelogram (2
  marks)
• Construct midpoints of diagonals (1 mark)
• Conclusion (1 mark)
• The diagonals intersect at their midpoints.
• The midpoints of the diagonals are the same point.

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Exercise 2 Question 2

• Construct a rectangle (1 mark)
• Proof that you constructed a rectangle (2 marks)
• Construct midpoints of diagonals (1 mark)
• Conclusions (2 marks)
• Diagonals of rectangles are the same length.
• Diagonals bisect each other (midpoints are the
  same)

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Exercise 2 Question 3

• Construct Rhombus (1 mark)
• Proof that you constructed rhombus (2 marks)
• Construct diagonals and midpoints of diagonals.
  (1 mark)
• Conclusions (2 marks)
• Diagonals bisect each other
• Diagonals are perpendicular

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Exercise 2 Question 4

• PQRS Square (3 marks)
• Side lengths all equal, 90 degree angle
• ABCD Rectangle (3 marks)
• 2 pairs of opposite sides equal, 90 degree angle
• JKLM Parallelogram (3 marks)
• 2 pairs of opposites sides equal, no 90 degree
  angle
• FGHI Rhombus (3 marks)
• All four sides are equal, no 90 degree angle.

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Exercise 2 - Question 5

• Create Quadrilateral 4 different sides and 4
  different angles (1 mark) - needed to show
  measurements
• Connect / Create midsegments (1 mark)
• Inside quadrilateral measurements (1 mark)
• side lengths, angles and diagonals
• Conclusions (1 mark)
• midsegments form a parallelogram

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Communication (10 marks)

• Organization of assignment
• Words / Text to explain
• Fit to Page
• Vertex / Coordinates labels match original
  assignment question
• Conclusions - Justified and Explained