- Tim Brzezinski
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. 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: 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 rhombus congruent? 2) Are opposite angles (ENTIRE ANGLES—like angle DAB & angle DCB) of a rhombus congruent? 3) Do the diagonals of a rhombus bisect EACH OTHER? 4) Does a diagonal of an rhombus bisect a pair of opposite angles? If so, how many diagonals do this? 5) Are the diagonals of a rhombus perpendicular? 6) Are the diagonals of a rhombus congruent? 7) Does either diagonal of a rhombus serve as a line of symmetry? If so, how many? 8) **Is a rhombus a parallelogram? If so, WHY is it a parallelogram? 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?