- Luke Cioffi
The applet below contains a quadrilateral that ALWAYS remains a kite. The purpose of this applet is to help you understand many of the geometric properties a kite has. Some of these properties are unique and only hold true for a kite (and not just any quadrilateral). 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 kite 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 diagonals of this kite. Label their point of intersection as “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 and display the following angles: BAD, ADC, DCB, & CBA. What, if anything, do you notice? 5) Measure & display the measures of the following angles: Angle BAE, EAD, ADE, EDC, DCE, ECB, CBE, EBA. What do you notice? 6) Measure display just one of the four angles you see with vertex E. 7) Construct polygon (triangle) ABC. Then reflect this polygon about diagonal AC. 8) Use GeoGebra to “UNDO” step (7). Now construct polygon (triangle) DBA. Then reflect this polygon about diagonal DB. Questions to answer/consider: 1) Are opposite sides of a kite congruent? 2) Are opposite angles (ENTIRE ANGLES—like angle DAB & angle DCB) of a kite ever congruent? If so, how many pairs of angles are congruent? 3) Do the diagonals of a kite bisect EACH OTHER? 4) Does a diagonal of a kite bisect a pair of opposite angles? If so, how many diagonals do this? 5) Are the diagonals of a kite perpendicular? 6) Are the diagonals of a kite congruent? 7) Does either diagonal of a kite serve as a line of symmetry? If so, how many?