First, students will learn what the third angle theorem is.
The Third Angle Theorem: Lesson (Geometry Concepts) by CK-12 Foundation
Next, students will learn why the third angle theorem is true. To understand the proof, students must know the angles in a triangle sum to \(180^\circ.\) The heart of the proof is realizing that if \(a + b + x = 180^\circ,\) and \(a + b + y = 180^\circ,\) then we can put those two equations together, yielding:$$a + b + x = a + b + y$$
Removing \(a + b\) from both sides, we find \(x = y.\)
Congruent Polygons & Third Angle Theorem by ProfRobBob
After that, students will learn how to use the third angle theorem. Here are some example problems:
Determine if the triangles below are similar (source).
Solve for \(x\) (source).
Here are two geometric problems. Students must know the vertical angles theorem and all the theorems involving parallel lines being intersected by a transversal.
Prove \(\triangle RSV \sim \triangle TUV\) (source).
Conclude by giving your students these challenges: