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Geometer Sketch Pad Assignment

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Geometer Sketch Pad Assignment

Mark Breakdown

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.

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

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

- 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

- 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!

- 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.

- 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)

- 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

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.

- 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

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