Copy of 6.2a SAS Inequality Theorem (Hinge Theorem)
Interactive exercises demonstrating the SAS inequality theorem (hinge theorem). Notice that "SAS inequality" refers to the hypothesis of the theorem, not the conclusion. That is, the hypothesis involves two pairs of congruent sides and a pair of incongruent included angles. The conclusion is not an inequality between angle measures. It is an inequality between the lengths of the third sides.
Exercise 1
Change and so that they are not equal. Observe what happens to the lengths of the opposite sides (BC and EF).
Exercise 2
Uncheck exercise 1 and check exercise 2. Drag Q, R, Y, and Z so that PQXY and/or PRXZ. Notice that although m<P > m<X, you are no longer able to use the SAS inequality theorem to say that QR>YZ!