Step-by-step explanation:
Use triangle congruency:
BC=EC, AC=DC - Given
m∠DCE = m∠ACB because they are vertical angles
Therefore ΔABC ≅ ΔDEC because of Side-Angle-Side congruency
AB=DE because corresponding parts of congruent triangles are also congruent (CPCTC)
The paragraph proof has been explained below to prove that Line BA = Line ED.
We are given;
BC = EC
AC = DC
This means that C is the midpoint of BE and AD.
Thus, according to vertically opposite angles theorem, we can say that;
m∠DCE = m∠ACB
This means we now have 2 corresponding sides that are equal and the included corresponding equal angle.
Therefore, we can deduce that ΔABC ≅ ΔDEC with SAS (Side-Angle-Side) congruency theorem.
Now, since ΔABC ≅ ΔDEC, we can say from (CPCTC) that AB = DE due to the fact that corresponding parts of congruent triangles are also congruent.
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