Question

Choose the Δ that seems to be congruent to the given one. [D - top left] [C - top right] [E - center] [A - bottom left] [B - bottom right] ΔBEC ≅ Δ AEB AED ABD (You guys are probably not gonna get to this in time so I'm putting this out there for the future of you that are gonna need it :) )

Answer 1

Δ BEC ≅ Δ AED

Explanation:

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.

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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