The applet below contains a quadrilateral that ALWAYS remains an isosceles trapezoid. The purpose of this applet is to help you understand many of the geometric properties an isosceles trapezoid has. Some of these properties are unique and only hold true for an isosceles trapezoid. 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 isosceles trapezoid around after completing each step in order to help you make more informed conjectures: [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 diagonals of this isosceles trapezoid. Label their point of intersection as “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 and display the following angles: BAD, ADC, DCB, & CBA. What, if anything, do you notice? [br]5) 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]6) Measure display just one of the four angles you see with vertex E. [br]7) Construct polygon (triangle) ABC. Then reflect this polygon about diagonal AC.[br]8) 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 an isosceles trapezoid congruent? [br]2) Are opposite angles (ENTIRE ANGLES—like angle DAB & angle DCB) of a isosceles trapezoid congruent?[br]3) An isosceles trapezoid has 2 pairs of BASE ANGLES (each pair is adjacent to one base of the trapezoid--ex: Angle BAD & Angle CBA form 1 pair of base angles). [br] Is there a relationship among the base angles of an isosceles trapezoid? If so, what is it? [br]3) Do the diagonals of an isosceles trapezoid bisect EACH OTHER?[br]4) Does a diagonal of an isosceles trapezoid bisect a pair of opposite angles? If so, how many diagonals do this? [br]5) Are the diagonals of an isosceles trapezoid perpendicular? [br]6) Are the diagonals of an isosceles trapezoid congruent?[br]7) Does either diagonal of an isosceles trapezoid serve as a line of symmetry? If so, how many?[br]8) Is a isosceles trapezoid a parallelogram? If so, WHY is it a parallelogram?