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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

translation
translation

reflection
reflection

dilation
dilation

rotation
rotation
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Answer 1

To determine the single rigid transformation that maps triangle \( \triangle ABC \) to triangle \( \triangle EDC \), we can analyze the congruence and positioning of the triangles.

Given that:

• \( \triangle ABC \) and \( \triangle EDC \) share vertex \( C \).
• Sides \( BC \) and \( CD \) are congruent.
• Angles \( A \) and \( E \) are congruent.
• Angle \( C \) is congruent in both triangles.

These properties suggest that \( \triangle ABC \) can be placed onto \( \triangle EDC \) through a specific transformation.

Since \( \angle C \) is a vertex common to both triangles and the two pairs of corresponding sides are congruent, a reflection across line segment \( CD \) would align the corresponding angles and sides.

Therefore, the correct transformation that maps \( \triangle ABC \) to \( \triangle EDC \) is:

reflection