The applet below contains a quadrilateral that ALWAYS remains a rhombus. The purpose of this applet is to help you understand many of the geometric properties a rhombus has. Some of these properties are unique and only hold true for a rhombus. The questions you need to answer are displayed below this applet.

Use GeoGebra to complete the following investigation. [b]BE SURE to move the vertices and sides of this rhombus 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:[br]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 rhombus congruent? [br]2) Are opposite angles (ENTIRE ANGLES—like angle DAB & angle DCB) of a rhombus congruent?[br]3) Do the diagonals of a rhombus bisect EACH OTHER?[br]4) Does a diagonal of an rhombus bisect a pair of opposite angles? If so, how many diagonals do this? [br]5) Are the diagonals of a rhombus perpendicular? [br]6) Are the diagonals of a rhombus congruent?[br]7) Does either diagonal of a rhombus serve as a line of symmetry? If so, how many?[br]8) **Is a rhombus a parallelogram? If so, WHY is it a parallelogram?[br]9) What properties are UNIQUE to a rhombus? That is, what properties ALWAYS hold true for a RHOMBUS but do NOT always hold true, in general, for a parallelogram?