Exploring isosceles trapezium properties
1) Explore the properties of an isosceles trapezium by dragging vertices A or B, or points X or Y. What do you notice about its angles, diagonals, symmetry, and sides? Does it have a circumcircle or incircle?
2) Write down your conjectures in relation to your observations in 1); then check your conjectures by completing this Isosceles Trapezium Quiz which will open in a new browser window. Continue until you get your % score and you are told you've completed the exercise. If you do not get 100%, repeat your dynamic exploration in 1) above.
3) Explain (prove) using the symmetry of the isosceles trapezium why your conjectures are true. After writing your explanations down, check and compare them with those in this exercise Isosceles Trapezium Properties Explanations.
Michael de Villiers, 3 October 2011.