Geometer Sketch Pad AssignmentMark 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 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

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

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

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

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

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

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

PQRS – Square (3 marks) Side lengths all equal, 90 degree angleABCD – Rectangle (3 marks) 2 pairs of opposite sides equal, 90 degree angleJKLM – Parallelogram (3 marks) 2 pairs of opposites sides equal, no 90 degree

angleFGHI – Rhombus (3 marks) All four sides are equal, no 90 degree angle.

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)

Organization of assignment Words / Text to explain Fit to Page Vertex / Coordinates labels match original

assignment question Conclusions - Justified and Explained