Students will learn how to use the hyperbolic identities to solve hyperbolic equations.
Solving hyperbolic equations
Concude by giving your students this challenge:
In the figure below, \(\overline{AB} = \overline{BC},\) and \(\overline{BF} = \overline{FD} = \overline{DE} = \overline{EC} = \overline{CA}.\) Find the measure of \(\angle x.\)
Here's the solution: First, use the isosceles triangle theorem to determine that \(\angle EDF = x.\) Next, use the exterior angle theorem to determine \(\angle DFE = x + x = 2x.\) Continue in this way. You will eventually find that \(\angle EAC = 4x.\) But \(\overline{BA} = \overline{BC}\) so invoking the isosceles triangle theorem one last time, we find \(\angle ACB = 4x\) as well. Finally, using the sum of interior angles for triangles theorem, we get the equation \(180^\circ = x + 4x + 4x.\) Solving for \(x,\) we find \(x = 20^\circ.\)