the image is two orange triangles one has abc written on them and the other had zyx. Triangle with abc is at the top and zyx triangle is at the bottom. abc

Question

a. What two transformations were completed to move triangle ABC to triangle XYZ? Include the name of the transformation and by how much. Example- it was Rotated by 180 degrees and reflected over line x=y

b. Are the shapes congruent? How do you know?

Answer 1

Based on your description of the image and the transformation of triangle ABC to triangle ZYX, here's how to analyze the situation:

a. Transformations:

1. Rotation: Triangle ABC was rotated by 180 degrees around a point. This means that every point of triangle ABC was turned around that point to create triangle ZYX.
2. Reflection: After the rotation, triangle ABC may have been reflected over a specific line (for example, the line y = x) to align it perfectly with triangle ZYX.

So, the transformations could be stated as:

• Rotated by 180 degrees around a point
• Reflected over a specific line (like y = x)

b. Congruence of Shapes: Yes, the shapes are congruent. Congruent shapes are those that have the same size and shape, which means their corresponding sides and angles are equal. Since triangle ABC was transformed through rigid transformations (rotation and reflection), the resulting triangle ZYX maintains all the properties of triangle ABC. Thus, both triangles are congruent because rigid transformations do not change the dimensions of the shapes.