Δ BEC ≅ Δ AED
Consider triangles BCA and ADB. Each of them share a common side, AB. Respectively each we should be able to tell that AD is congruent to BC, and DB is congruent to CA, so by SSS the triangles should be congruent.
So another possibility is triangles BEC, and AED. As you can see, by the Vertical Angles Theorem m∠BEC = m∠ADE, resulting in the congruency of an angle, rather a side. As mentioned before AD is congruent to BC, and perhaps another side is congruent to another in the same triangle. It should be then, by SSA that the triangles are congruent - but that is not an option. SSA does is one of the exceptions, a rule that is not permitted to make the triangles congruent. Therefore, it is highly unlikely that triangles BEC and AED are congruent, but that is what our solution, comparative to the rest.
Δ BEC ≅ Δ AED this is our solution
bad or dab .
Triangles are labelled by stating all of its vertices, usually capital letters. Triangle FGA is made of the vertices called F, G and A.
For two triangles to be congruent, they must have all equal angles and equal sides. Although, you don't need to have all sides and angles information to determine if they are congruent.
Out of the three other triangles, triangle ABG has letters G and A in common with FGA. From this, we assume they both have at least two angles ( G and A ) and one side (GA) that are the same.
Therefore they might have ASA (angle side angle) similarity, which is one of the ways to tell if two triangles are congruent.
Three of the six pieces of information for angle or side are usually enough to determine if triangles are congruent (But not AAA similarity).