# Converse of each corresponding angles theorem

The corresponding angles theorems include theorems such as the alternate interior angles theorem. These theorems are typically taught as part of a high-school geometry curriculum. A good curriculum will also include the proof of each theorem. However, what I have yet to see, is a curriculum that covers the converse of each theorem and their proofs. This is not too difficult for high-school students. The method of contradiction is often used in geometry, and this is the most advanced concept required to understand these proofs. In fact, the method of contradiction is only used to prove the converse of the corresponding angles postulate. After that, the converse of each corresponding angle theorem follows easily. Here are videos covering each proof:

- Proof: Converse of the corresponding angles postulate
- Proof: Converse of the consecutive interior angles theorem
- Proof: Converse of the alternate interior angles theorem
- Proof: Converse of the alternate exterior angles theorem

It may be interesting to students that the method used for proving the converse of the corresponding angles postulate can also be used for the converse of each theorem. Here's a proof for each: