It means they are the same, but they could be rotated differently, or the arms of one may stretch longer than the other. Just as long as the measurement of the angle is the same. e.g., two right angles (90 degree angles), but one of them has the arms facing up and to the right, and one of them facing so that the arms are pointing down and to the left.
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Two angles that are congruent have the same angle measurement.
Two angles are congruent if they both measure exactly the same number of degrees. Two line segments are congruent if they both have exactly the same length.
Yes, because of the base angles theorem converse: If two angles in a triangle are congruent, then the sides opposite the angles are congruent.
yes
Vertical angles are always, by definition, congruent. Note: If the two vertical angles are right angles then they are both congruent and supplementary.