The triangles are congruent by the SSS congruence theorem.

Question

Triangles A B C and D E C are connected at point C. Triangle A B C is reflected across B C and then is rotated about point C to form triangle D E C.

Which rigid transformation(s) can map TriangleABC onto TriangleDEC?

reflection, then rotation
reflection, then translation
rotation, then translation
rotation, then dilation

Answer 1

To determine which rigid transformation(s) can map Triangle ABC onto Triangle DEC, let's analyze the scenario step-by-step.

1. Reflection Across BC: When Triangle ABC is reflected across line BC, the image triangle will be congruent to Triangle ABC and will share point C. Let's denote this reflected triangle as Triangle A'B'C.

2. Rotation About Point C: After reflecting Triangle ABC, we then rotate the reflected Triangle A'B'C around point C to get Triangle DEC. Since Triangle DEC is formed by applying these two transformations, it indicates that the mapping from Triangle ABC to Triangle DEC can be achieved by first reflecting and then rotating.

Now, considering the options:

• Reflection, then rotation: This accurately describes the process used to obtain Triangle DEC from Triangle ABC.
• Reflection, then translation: This is incorrect because we are rotating, not translating.
• Rotation, then translation: This is incorrect as we don't perform a translation after rotation.
• Rotation, then dilation: This isn’t applicable since we are not dilating.

Thus, the correct transformation(s) to map Triangle ABC onto Triangle DEC is:

Reflection, then rotation.