# Which Composition Of Similarity Transformations Maps Polygon Abcd To Polygon A’b’c’d’?

### INTRO:

Similarity transformations are a type of transformation that preserves the shape and size of an object. These transformations can be used to map one polygon to another. In this article, we will look at which combination of similarity transformations can be used to map polygon ABCD to polygon A’B’C’D’.

### Understanding the Transformations

Similarity transformations consist of three types of transformations: translations, rotations, and scaling. Translations involve moving an object in a certain direction while keeping its shape and size. Rotations involve rotating an object around a certain point while keeping its shape and size. Scaling involves enlarging or reducing the size of an object while keeping its shape.

These transformations can be combined to form a single transformation. For example, a translation followed by a rotation and then a scaling can be combined into a single transformation. This combination of transformations can be used to map one polygon to another.

### Mapping Polygon Abcd to Polygon A’b’c’d’

To map polygon ABCD to polygon A’B’C’D’, we need to use a combination of similarity transformations. First, we need to translate polygon ABCD so that its vertices are in the same position as the vertices of polygon A’B’C’D’. Then, we need to rotate polygon ABCD so that its sides are in the same orientation as the sides of polygon A’B’C’D’. Finally, we need to scale polygon ABCD so that its sides are the same length as the sides of polygon A’B’C’D’.

Once these transformations have been applied, polygon ABCD will be identical to polygon A’B’C’D’. This combination of transformations is the only way to map one polygon to another while preserving its shape and size.

### OUTRO:

In conclusion, a combination of similarity transformations can be used to map polygon ABCD to polygon A’B’C’D’. This combination consists of a translation, a rotation, and a scaling. By applying these transformations, we can ensure that the two polygons are identical in shape and size.