(3 points)

Question

Two transformations were performed on Triangle ABC. The first transformation was a reflection over the
. The second transformation was a
. The second transformation was

and

.
Question 2
(1 point)
Are the shapes congruent? How do you know?
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Answer 1

To determine the congruence of Triangle ABC after two transformations, we need to clarify a few details about the transformations and their effects on the triangle.

1. First Transformation: Reflection

   • A reflection over a line (such as the x-axis, y-axis, or any line in the plane) creates a mirror image of the triangle. Reflections preserve lengths and angles, meaning the resulting shape will have the same size and shape as Triangle ABC.

2. Second Transformation: Transformation Type

   • The second transformation you've mentioned is unclear since you left a gap. It could be a rotation, translation, or another reflection. Here’s how different transformations affect congruence:
     • Rotation: Rotating the triangle around a point also preserves lengths and angles, resulting in a congruent shape.
     • Translation: Moving the triangle without changing its orientation maintains congruence.
     • Another Reflection: If another reflection is applied (even over a different line), it also keeps the triangle congruent.

In conclusion:

Are the shapes congruent?

Yes, the shapes are congruent. Both transformations (the reflection and the second transformation, whatever it may be) preserve the side lengths and angles of the original triangle. Therefore, Triangle ABC and the final shape are congruent.