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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 ?

Answer 1

To determine what single rigid transformation maps triangle \( ABC \) to triangle \( EDC \), we need to analyze the given information and the congruence of the corresponding parts of the triangles.

1. Congruent Sides: It is given that the sides \( BC \) and \( CD \) are congruent.

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

Given these points of congruence, we can conclude that triangles \( ABC \) and \( EDC \) are congruent by the Angle-Side-Angle (ASA) postulate.

To find the transformation:

1. We see that \( BC \) (from \( ABC \)) is congruent to \( CD \) (from \( EDC \)), showing they have the same length.
2. Both triangles share the side \( AC \) and vertex \( C \), and we know angles at \( C \) are congruent.

This suggests that to map triangle \( ABC \) to triangle \( EDC \), we can use a rotation around point \( C \). Specifically, if you rotate triangle \( ABC \) around point \( C \) by the appropriate angle that aligns angle \( A \) with angle \( E \), the corresponding vertices and sides will line up perfectly due to the congruence and shared vertex.

Therefore, the single rigid transformation that maps triangle \( ABC \) to triangle \( EDC \) is a rotation around point \( C \).