2 triangles, upper A upper B upper C and upper C upper D upper E are shown. Both share vertex upper C. Sides upper B upper C and upper C upper D are congruent. Angles upper A and upper E are congruent. Angle upper C is congruent in both the triangles.

Question

What single rigid transformation maps △ABC→△EDC ?

(1 point)
Responses

dilation
dilation

rotation
rotation

translation
translation

reflection

Answer 1

To determine the rigid transformation that maps triangle \( ABC \) to triangle \( EDC \) under the given conditions, let's analyze the information:

1. Shared Vertex and Congruent Angles: Both triangles share vertex \( C \) and the angles \( \angle A \) and \( \angle E \) are congruent, as well as \( \angle C \) in both triangles.

2. Congruent Sides: The sides \( BC \) and \( CD \) are also congruent.

This setup suggests that the triangles \( ABC \) and \( EDC \) are congruent triangles with corresponding angles and sides. Since angles \( A \) and \( E \), along with angle \( C \) are equal, and sides \( BC \) and \( CD \) are congruent, we can conclude that the triangles are similar or congruent.

Given that \( C \) is a common vertex and that we have congruent angles and sides, one possible transformation that can map one triangle to another is a reflection across the line that bisects \( C \) if \( A \) and \( E \) are positioned in such a way that they reflect into each other.

Since the only matching feature we can directly observe from the provided information is that angles \( A \) and \( E \) are congruent and \( C \) is shared, we can confirm that the transformation to go from triangle \( ABC \) to triangle \( EDC \) would likely be a reflection.

Thus, the correct response is:

reflection