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Question

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.

What single rigid transformation maps △ABC→△EDC ?

(1 point)
Responses

rotation
rotation

translation
translation

dilation
dilation

reflection

Answer 1

To determine the single rigid transformation that maps triangle \( \triangle ABC \) to triangle \( \triangle EDC \), we can analyze the given information:

1. The triangles share the vertex \( C \).
2. The sides \( BC \) and \( CD \) are congruent.
3. Angles \( A \) and \( E \) are congruent.
4. Angle \( C \) is congruent in both triangles.

Since angles \( A \) and \( E \) are congruent and angle \( C \) is shared (also congruent), along with the congruency of the sides \( BC \) and \( CD \), this indicates that both triangles are similar and can be related by rotation.

To map \( \triangle ABC \) to \( \triangle EDC \), you would need to rotate \( \triangle ABC \) around point \( C \) to align with \( \triangle EDC \).

Thus, the correct transformation is:

rotation