Euclidean geometry/Congruency

Congruency

 * Two things are congruent if they are the same. Okay, onto next topic...
 * Wait a second; we didn't define that very well! That's okay. Congruency is a thing that is defined for everything that is used in geometry. For example, congruency can be defined for peanut butter jars


 * Two jars of peanut butter are congruent if and only if they have jars of the same shape, are filled to the same height with peanut butter, and the peanut butter tastes the same for both jars.


 * You could do a similar thing for gumballs, but that wouldn't be relevant to geometry, unlike peanut butter jars. Every element of geometry has its own definition of congruence.


 * This is the symbol of congruence.


 * $$\cong$$


 * Now for some congruency definitions!


 * Two line segments are congruent if and only if they have equal lengths.


 * Two angles are congruent if and only if their measures of the angles are equal.


 * Two points, lines, rays, or planes have no congruency definition.


 * Actually, those three definitions will do for now!