Use GeoGebra to complete the following investigation. [b]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[/b]: [br][br]1) Measure and display the lengths of all 4 sides. What, if anything, do you notice? Describe in detail. [br]2) Construct the midpoint of segment AC (even though you haven’t constructed segment AC yet.) Label this point “E”. [br]3) Construct segments with lengths AE, BE, CE, & DE. Then measure and display their lengths. What do you notice? Describe in detail. [br]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. [br]5) Measure display just one of the four angles you see with vertex E. [br]6) Construct polygon (triangle) ABC. Then reflect this polygon about diagonal AC.[br]7) Use GeoGebra to “UNDO” step (6) and step (5). Now construct polygon (triangle) DBA. Then reflect this polygon about diagonal DB. [br][br]Questions to answer/consider: [br][br]1) Are opposite sides of a parallelogram congruent? [br]2) Are opposite angles (ENTIRE ANGLES—like angle DAB & angle DCB) of a parallelogram congruent?[br]3) Do the diagonals of a parallelogram bisect EACH OTHER?[br]4) Does a diagonal of an parallelogram bisect a pair of opposite angles? If so, how many diagonals do this? [br]5) Are the diagonals of a parallelogram perpendicular? [br]6) Are the diagonals of a parallelogram congruent?[br]7) Does either diagonal of a parallelogram serve as a line of symmetry? If so, how many?
[color=#000000]Please use these applets to help you complete the [/color][i][color=#0000ff]Parallelogram Investigation[/color][/i][color=#000000] questions given to you at the beginning of class. [/color]
Sides of a Parallelogram
Interior Angles of a Parallelogram
Diagonals of a Parallelogram
Quadrilateral Interior & Exterior Angle Sum Theorems (V2)
[b]Directions:[/b][br][br]Mess around with the applet below for a few minutes. [br]As you do, [color=#b20ea8][b]BE SURE TO DRAG THE PINK VERTICES around[/b][/color]. [br][br]After interacting with this applet, please answer the questions that appear below it.
[b][color=#c51414]Questions:[/color][/b][br][br]1) What can you conclude about the [b]sum of the interior angle measures[/b] of a quadrilateral? Explain how you came to this conclusion.[br]2) What can you conclude about the [b]sum of the exterior angle measures[/b] of a quadrilateral? Explain how you came to this conclusion.