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Comprehensive Geometry Assignment Breakdown on Medians, Bisectors, and Quadrilaterals

This assignment focuses on key geometric concepts, including medians, bisectors, and altitudes, while providing step-by-step exercises to enhance understanding. Students will plot points to create segments, calculate midpoints, and analyze various triangles, including scalene and isosceles forms. They will construct polygons like parallelograms and rectangles and explore relationships between side lengths, angles, and diagonals. With clear expectations for proof and conclusions, this assignment also emphasizes effective communication and organization in presenting geometric concepts.

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Comprehensive Geometry Assignment Breakdown on Medians, Bisectors, and Quadrilaterals

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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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