Students will see two proofs that the sum of angles in a triangle is \(180^\circ\). The first proof is a paper-cutting proof, which is informal, but is intended to increase their confidence in the theorem. The second proof is a more formal geometric proof. It works by drawing a line which is parallel to the base, through the apex of the triangle, then making some deductions. Students will see problems where a triangle is given with a variable relating its angles by linear expressions. For example, the angles might be \(x, 2x - 30\), and \(90\). Knowing that a triangle's interior angles sum to \(180^\circ\), make an equation whose LHS is the sum of the three angles and whose RHS is \(180\). Then use algebra to solve for the value of the variable, from which all angle measures can be determined.
Conclude by leading this investigation:
Which came first: Chicken or Egg