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# Geometer Sketch Pad Assignment - PowerPoint PPT Presentation

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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Presentation Transcript

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.

• 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