What Makes Angles Congruent?

Congruent angles have the same angle (in degrees and radians, both are units of measure for angles).

Angles are congruent as long as the angles are the same, they don't have to point in the same direction, they don't have to be made with lines of the same length. You can see an example below:

We sometimes have congruent angles in shapes. It is important to have a way of notating the congruent angles--this helps us understand properties of the shapes. You will start noticing the benefits of notation later on.

We usually put an equal amount of short lines on congruent angles. For example, angle S and W are congruent, and they are both marked by two short lines. Angle R and X are congruent and they are both marked by one short line. Similarly, we can also notate equal lines. Line RS and XW are equal, so they are both marked by three short lines.

Angle congruence is when at least two angles have the same measure. So if the below angles were formed...

We now know that the angles are congruent. By definition, congruence means that two angles having the same measurement. So measure equality is a must when you need to prove two angles are congruent. By the way, NEVER assume that an angle is a whatever kind of angle. It's one of the most fundamental rules of geometry.

Congruent angles have the same angle measure. The orientation of the angles doesn't matter, the length of the sides doesn't matter, only the angle measure.

Notation $$\\$$ We use $\cong$ to denote congruence. If two angels are congruence, we write, for example: $$\angle ABC \cong \angle DEF$$

We usually mark the congruent angels with a little arc. If there are multiple pairs of congruent angles, we can vary how we draw the arc--double arc, triple arc, dashed line arc, etc.

Think you have a handle on this? Try the following problem!