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Explanation:
Marked sides are congruent. Shared sides are congruent. Marked angles are congruent. Vertical angles are congruent. The postulates available for proving congruence are ...
AAS, ASA, SAS, SSS
where the S stands for corresponding congruent sides, and the A stands for corresponding congruent angles.
For right triangles, there is also the HL theorem, where H is the hypotenuse and L is one leg.
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1) AAS; right angle, vertical angle, marked sides
2) SSS; 2 marked sides, shared side
3) SAS; marked side, vertical angle, marked side
4) HL; hypotenuse and leg are marked
5) not congruent (need at least one side in addition to angles)
6) ASA; marked angle, marked side, vertical angle
7) SSS; 3 marked sides
8) SAS; marked side, marked angle, shared side
9) HL; hypotenuse and shared side
10) not congruent (need at least two angles with one side)
11) ASA; right angle, shared side, marked angle
12) AAS; two marked angles (in the same order), marked side
