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Geometer Sketch Pad Assignment

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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  1. Geometer Sketch Pad Assignment Mark Breakdown

  2. 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.

  3. 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

  4. 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

  5. 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

  6. 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!

  7. 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.

  8. 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)

  9. 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

  10. 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.

  11. 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

  12. 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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