Pythagorean Theorem. When Is The Best Time To Teach It?

  Today, I reviewed the distance formula in preparation for the semester final.  It got me to thinking when in the semester should I teach the Pythagorean theorem?

If I teach it at the beginning of the year when I do midpoint and distance, then it is quite applicable for distance. 

If I wait till later in the semester when I'm doing trig ratio's then I've missed the chance to relate the distance formula to it. 

I like to teach the Pythagorean theorem just after I teach classification of triangles, congruent and similar triangles because I have students use the  equal, less than or greater than to tell the type of triangle based only on measurements.

I love the theorem because it has so many possible applications from vectors to televisions to physics and it is good for them to know the basic formula.  Perhaps, this needs to be taught at different points throughout the geometry class with different applications so students see the formula as the course progresess.

Some real life applications include:
1. Road trips - finding the shortest route.
2. Painting buildings to help find the right sized ladder.
3. TV's and Computer Monitors
4. Navigation.
5. Surveying.

So if I consider that it is better to teach the theorem at several points throughout the course and I include the appropriate real life examples, then it might help students learn to use the theorem better and become familiar with it outside of the theoretical state.

If you have any suggestions, I'd love to hear from you.