The AAS Congruence Theorem Quick Check

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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

dilation
dilation

translation
translation

reflection
reflection

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 given information:

1. Congruent Angles: Angles \( A \) and \( E \) are congruent, and angle \( C \) is congruent in both triangles.
2. Congruent Sides: Sides \( BC \) and \( CD \) are congruent.

Since both triangles share the same angle \( C \) and have congruent angles at \( A \) and \( E \), it appears that triangles \( \triangle ABC \) and \( \triangle EDC \) are congruent by the Angle-Angle-Side (AAS) criterion.

To determine the specific transformation, we consider the following options:

• Dilation: This changes the size of the figure, which is not applicable here as we are looking for a congruence transformation.
• Translation: This would shift the triangle to a different location without changing its orientation.
• Reflection: This would flip the triangle over a line, changing the orientation.
• Rotation: This would rotate the triangle around a point.

Given that the sides \( BC \) and \( CD \) are congruent and that they share angle \( C \), a rigid transformation that could map one triangle onto the other involves using rotation, considering that we need to align the two triangles together while maintaining the congruence.

Therefore, the correct answer is:

rotation