5.6 Hinge Theorem and its Converse
Hinge Theorem (Inequalities in 2 Triangles)
What's the relation between side AB to side DE, and BC to EF?
Move vertices C and F. What conclusion can you make when angle B is greater than angle E? Hint: observe the side opposite to angles B and E.
This is an example of Hinge theorem. Play around with the triangle. Another name for the Hinge Theorem is SAS inequality. Why do you think it is also called SAS Inequality?
What conclusions can you make about angles B and E when side DF is greater than side AC?
Another name for the Converse of the Hinge Theorem is SSS inequality. Why do you think it is also called SSS Inequality?