Answer:
A) triangle ABC is congruent to triangle EDC
Explanation:
The AAS method of proving congruence of triangles uses two angles and a non-included side of the triangle. If two angles and the non-included side of a triangle are congruent to the corresponding parts of another triangle, then the triangles are congruent.
Let's see what we have in this problem:
<ACB and <ECD are congruent since they are vertical angles.
<A and <E are congruent by given.
Sides AB and ED are non-included sides and are congruent.
Since we have two angles and a non-included side of a triangle and the corresponding parts of another triangle, the triangles are congruent by AAS.
Now we need the statement of congruence.
Angles ACB and ECD are corresponding angles, so the letter C must appear in both triangles in the same position.
Angles A and E are corresponding angles, so the letters A and E must appear in both triangles the same position.
We already have CA and CE. The last angles left are corresponding angles B and D, so we get triangle CAB and triangle CED. Since a triangle may be named using any order of the vertices, we can rename the triangles ABC and EDC and maintain the same corresponding vertices.
Answer: A) triangle ABC is congruent to triangle EDC