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

To determine the transformations that move triangle ABC to triangle XYZ, you would typically follow these steps:

1. Identify the positions of the vertices of triangle ABC and triangle XYZ to understand how they relate to each other.
2. Look for any similarities in the angles and side lengths of both triangles, which could suggest transformations such as rotations, translations, or reflections.
3. Apply the specific transformations one by one and observe whether the triangles coincide after these transformations.

For example, if after analyzing the two triangles, you found that triangle ABC was:

• Reflected over line y = x and then
• Translated 3 units to the right and 2 units up,

You would state:

• "Triangle ABC was reflected over line y = x and translated 3 units right and 2 units up."

Regarding whether the shapes are congruent:

• Yes, triangle ABC and triangle XYZ are congruent if the transformations used to map one triangle onto the other are rigid transformations (i.e., transformations that preserve distances and angles). Reflections, rotations, and translations are all rigid transformations. Therefore, if triangle ABC can be moved to coincide with triangle XYZ through these transformations, then they are congruent. We can verify this by checking that their corresponding sides and angles are equal.

If you have specific coordinates for triangles ABC and XYZ, or further details about their configurations, I could provide a more precise answer regarding the transformations involved and their congruence.