2.3 Angle Relationships

Similar to the ruler postulate, the protractor postulate simply states that we can measure angles (and that for our purposes, those angle measures are positive - no matter which direction we measure from - which is why there are two set of numbers on a protractor!).

Also like its counterpart, the segment addition postulate from yesterday, the angle addition postulate is really telling us that the sum of the measure of two angles make the measure of the larger angle.

The angle addition postulate can be combined with the ideas of complementary (add to 90 deg.) and supplementary (add to 180 deg.) to give us the supplement theorem and complement theorem. These are just special cases of the angle addition postulate where the sum happens to be 90 or 180. Because these have been proven to always be true, they are considered theorems and not just the angle addition postulate.

The first words (reflexive, symmetric, and transitive) should be a bit familiar!

These two theorems are really just extensions of the Transitive property of congruence....but someone felt that it was necessary to call your attention to them specifically.

Remember when we talked about the type of angles in the last unit, we mentioned that vertical angles are always congruent. **This is a theorem that you MIGHT be asked to prove on the summative :-)

These 5 theorems might all seem like common sense, but remember that they have been proven so that we can build on only thoughts that are supported by proof or postulate.