Two or more triangles are said to be congruent if and only if they have equal lengths of sides and equal measures of angles.
Thus, the required proof is as shown below:
STATEMENTS REASONS
1. ΔABC and ΔDEC with AB ≅ DE;
BC ≅ EC; <1 ≅ <2 Given
2. <1 and < ABC; < 2 and <DEC are sup Sum of angles on a straight line
3. <ABC ≅ <DEC Congruent angles of similar triangles
4. ∴ΔABC ≅ ΔDEC Side-Angle-Side (SAS) postulate
5. ∴<ACB ≅ <DCE CPCTC postulate
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