- Tim Brzezinski
Use GeoGebra to complete the following investigation. BE SURE to move the vertices and sides of this parallelogram around after completing each step in order to help you make more informed conjectures: 1) Measure and display the lengths of all 4 sides. What, if anything, do you notice? Describe in detail. 2) Construct the midpoint of segment AC (even though you haven’t constructed segment AC yet.) Label this point “E”. 3) Construct segments with lengths AE, BE, CE, & DE. Then measure and display their lengths. What do you notice? Describe in detail. 4) Measure & display the measures of the following angles: Angle BAE, EAD, ADE, EDC, DCE, ECB, CBE, EBA. What do you notice? Describe in detail. 5) Measure display just one of the four angles you see with vertex E. 6) Construct polygon (triangle) ABC. Then reflect this polygon about diagonal AC. 7) Use GeoGebra to “UNDO” step (6) and step (5). Now construct polygon (triangle) DBA. Then reflect this polygon about diagonal DB. Questions to answer/consider: 1) Are opposite sides of a parallelogram congruent? 2) Are opposite angles (ENTIRE ANGLES—like angle DAB & angle DCB) of a parallelogram congruent? 3) Do the diagonals of a parallelogram bisect EACH OTHER? 4) Does a diagonal of an parallelogram bisect a pair of opposite angles? If so, how many diagonals do this? 5) Are the diagonals of a parallelogram perpendicular? 6) Are the diagonals of a parallelogram congruent? 7) Does either diagonal of a parallelogram serve as a line of symmetry? If so, how many?