Practice problems (do not hand in):

Venema 1.1.1, 1.1.2, Example pg 16-17, 1.2.1, 1.2.2, 1.3.1

 

Homework problems (to hand in):

  1. Perform the GeoGebra construction described in exercise 1.3.2. On paper, draw a diagram describing what you witnessed in the drag test in GeoGebra. Answer the question asked in the exercise by making a conjecture about the area of a triangle. Prove your conjecture.
  2. Perform the GeoGebra construction described in exercise 1.3.3. On paper, draw a diagram describing what you witnessed in the drag test in GeoGebra. Make a conjecture about the sum of interior angles of a triangle. Prove your conjecture.
  3. Perform a construction in Geogebra which is analogous to exericise 1.3.3, but replace the triangle with a quadrilateral. On paper, draw a diagram describing what you witnessed in the drag test in GeoGebra. Make a conjecture about the sum of interior angles of a quadrilateral. Prove your conjecture. (Hint: use your result from 1.3.3.)
  4. Perform a construction in Geogebra which is analogous to exericise 1.3.3, but replace the triangle with a pentagon. On paper, draw a diagram describing what you witnessed in the drag test in GeoGebra. Make a conjecture about the sum of interior angles of a pentagon. Prove your conjecture. (Hint: use your result from 1.3.3.)
  5. State and prove a conjecture about the interior angles of an n-gon, for any n. (Hint: you are generalizing the work you did in exerices 2, 3, and 4 above.)