the symbol for congruent is ~ with _ in the same space. (US keyboard does not have a congruent key
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Two angles that are congruent have the same angle measurement.
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.
Once you have shown that two triangles are congruent you can use CPCTC (corresponding parts of congruent triangles are congruent) to show the congruence of the remaining sides and angles.