Geometer sketch pad assignment
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Geometer Sketch Pad Assignment. Mark Breakdown. 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

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Geometer Sketch Pad Assignment

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Geometer sketch pad assignment

Geometer Sketch Pad Assignment

Mark Breakdown


Exercise 1 question 1

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.


Geometer sketch pad assignment

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


Exercise 1 question 2

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


Exercise 1 question 3

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


Exercise 1 question 4

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!


Exercise 2 question 1

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.


Exercise 2 question 2

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)


Exercise 2 question 3

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


Exercise 2 question 4

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.


Exercise 2 question 5

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


Communication 10 marks

Communication (10 marks)

  • Organization of assignment

  • Words / Text to explain

  • Fit to Page

  • Vertex / Coordinates labels match original assignment question

  • Conclusions - Justified and Explained


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