Question

Explanations Needed (In-Depth)

I need explanations for Properties of Dilations and Similarity and Similarity Transformations.
I am in 10th-grade Geometry, Thank you so much!

Answer 1

Properties of Dilation

• Each angle of the figure is the same. Midpoints of the sides of the figure remain the same as the midpoint of the dilated shape. Parallel and perpendicular lines in the figure remain the same as the parallel and perpendicular lines of the dilated figure. The images remain the same.

• Similarity. In order for two figures to be similar, they must have congruent (equal) corresponding angle measures and proportional sides. Dilations create similar figures because multiplying by the scale factor creates proportional sides while leaving the angle measure and the shape the same.

• A similarity transformation is one or more rigid transformations (reflection, rotation, translation) followed by a dilation. When a figure is transformed by a similarity transformation, an image is created that is similar to the original figure. ... In general, similarity transformations preserve angles.

• A dilation stretches or shrinks a figure. The image created by a dilation is similar to the original figure. The scale factor of a dilation is the ratio of corresponding side lengths. In this course, the center of dilation will always be the origin.

Dilations in Animation

• The three basic rigid motions are translations, reflections, and rotations. In addition to being rigid motions, these are also considered transformations. Transformations change the location or orientation of an image but not the shape.

• Isometric transformations have the same shape AND size, similarity transformations just have the same shape. Isometric transformations have the same shape AND size, similarity transformations just have the same size. They are the same, no differences. ... A stretch is not a similarity transformation.

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