The triangles ABC and DEC are congruent by AAS(Angle-Angle-Side). The second option is correct.
What is congruent?
Two triangles are said to be congruent if all three corresponding sides are equal and all three corresponding angles are the same size.
What is AAS?
Angle-Angle-Side (AAS) is an acronym for Angle-Angle-Side. When two angles and a non-included side of one triangle are equivalent to the corresponding angles and sides of another triangle, the triangles are said to be congruent.
What are vertical angles?
When two lines intersect at a point, vertical angles are formed which are always equal to each other.
How to solve this problem?
Given that the side BC in triangle ABC and the side CE in triangle DEC are equivalent. Also, angle A in triangle ABC and angle D in triangle DEC are equivalent. Notice that angle C in triangle ABC and angle C in triangle DEF are vertical angles. Therefore from the above AAS rule, it can be concluded that the triangles ABC and DEC are congruent.
Therefore, the triangles ABC and DEC are congruent by AAS(Angle-Angle-Side). The second option is correct.
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