Which composition of transformations will create a pair of similar, not congruent triangles?
A. a rotation, then a reflection
B. a translation, then a rotation
C. a reflection, then a translation
D. a rotation, then a dilation

The correct composition of transformations that creates similar but not congruent triangles is a rotation followed by a dilation. Rigid transformations (like reflection and rotation) preserve size and shape, leading to congruency, while dilation changes the size but keeps the shape, creating similarity. Thus, the answer is option D: a rotation, then a dilation.
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Answered by Anonymous | 2025-07-04

Rigid transformations (rotation, reflection, translation) produce congruent figures.
Dilation changes the size but preserves the shape, creating similar figures.
A rotation followed by a dilation results in similar, not congruent triangles.
The correct answer is a rotation, then a dilation: a rotation, then a dilation ​

Explanation

Analyze the transformations Let's analyze the options to determine which composition of transformations will create similar, but not congruent triangles. Remember that:


Rigid transformations (rotation, reflection, translation) preserve size and shape, resulting in congruent figures.
Non-rigid transformations (dilation) change the size but preserve the shape, resulting in similar figures.


Evaluate each option


Option 1: a rotation, then a reflection Both rotation and reflection are rigid transformations. Therefore, this composition will result in congruent triangles.
Option 2: a translation, then a rotation Both translation and rotation are rigid transformations. Therefore, this composition will result in congruent triangles.
Option 3: a reflection, then a translation Both reflection and translation are rigid transformations. Therefore, this composition will result in congruent triangles.
Option 4: a rotation, then a dilation Rotation is a rigid transformation, and dilation is a non-rigid transformation that creates similar figures. Therefore, this composition will result in similar, not congruent triangles.


Select the correct option The composition of a rotation followed by a dilation will create a pair of similar, not congruent triangles.

Examples
Imagine you have a photograph. If you rotate the photo, it's still the same size and shape – just turned. If you then enlarge (dilate) the rotated photo on a photocopier, the new photo is similar to the original but a different size. This is an example of transformations creating similar, not congruent figures.

Answered by GinnyAnswer | 2025-07-04