Can the two triangles be proved congruent? If so, by which method: sss, sas, asa, aas, or hl. Please help me with this problem.Can the two...

Triangles are congruent if they have three equal sides and
three equal internal angles.  Congruent triangles can be exact copies or mirror
images.

Here are the rules for congruent
triangles:

1.  SSS:  all three sides are
equal

2.  SAS:  two sides and their included angle are
equal

3.  ASA: a pair of angles and their included side is
equal

4.  AAS: a pair of corresponding angles and a
non-included side is equal

5.  HL:  two right triangles are
congruent if their hypotenuse and 1 leg are equal

In image
1, the triangles are congruent (although mirror images) because they have three equal
sides (shown by the 1, 2 and 3 hash marks).  Thus their congruency is proved by
SSS.

In image 2, both triangles have their shortest sides
equal (indicated by double hash marks).

Both triangles
share the marked angle.

This angle is shared by the
shortest sides already mentioned, plus equal longer sides the lengths of which are the
sum of a single and a double hash mark.

Thus, the triangles
in image 2 are congruent based on SAS.  As in image 1, the congruent triangles are
mirror images.