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Vocabulary Similarity transformations Congruence transformations

Learn to identify transformations as similarity or congruence transformations. Vocabulary Similarity transformations Congruence transformations Artists and graphic designers often

use repeated geometric shapes to create a work of art, a company logo, or a pattern for wallpaper or fabric. They use transformations to vary the shape, size, and position of the figures, making a pleasing design. *Transformations that result in an image that is the same shape and the same size as the original are congruence transformations. *Transformations that result in an image that is the same shape as the original, but a different size are similarity transformations. A dilation produces an image that is similar to the original.

Remember! Additional Example 1: Identifying Similarity Transformations

Identify the transformation from the original to the image, and tell whether the two figures are similar or congruent. Original ABCD: A(1, 1), B(2, 1), C(2, 2), D(1, 2) Image A'B'C'D': A'(3, 3), B(6, 3), C'(6, 6), D'(3, 6) The coordinates of A, B, C, and D are triple the original coordinates A, B, C, and D. So the transformation is a dilation and the squares are similar. Check It Out: Example 1 Identify the transformation from the original to the image, and tell whether the two figures are similar or congruent. Original ABCD: A(1, 1), B(2, 1), C(2, 2), D(1, 2) Image A'B'C'D': A'(2, 2), B(4, 2), C'(4, 4), D'(2, 4) The coordinates of A, B, C, and D are triple the original coordinates A, B, C, and D. So the transformation is a dilation and the squares are similar. Helpful Hint Rotations, translations, and reflections do not

change the size or shape of a figure. Helpful Hint Additional Example 2: Identifying Congruence Transformations

Identify each transformation from the original to the image, and tell whether the two figures are similar or congruent. A. Original ABCD: A(2, 5), B(1, 4), C(1, 1), D(2, 1) Image A'B'C'D': A'(5, 2), B'(4, 1), C'(1, 1), D'(1, 2) 90 rotation clockwise; congruent Additional Example 2: Continued

B.Original ABC: A(1, 3), B(2, 1), C(3, 1)Image A'B'C': A'(1, 1), B'(2, 5), C'(3, 3) Translation 4 units up; congruent Additional Example 2: Continued

C.Original ABC: A(1, 2), B(1, 3), C(2, 2)Image A'B'C': A'(1, 2), B'(1, 3), C'(2, 2) Reflection across the x-axis; congruent Check It Out: Example 2 Identify each transformation from the original to the image, and tell whether the two figures are similar or congruent. Original ABC:A(1, 3), B(2, 1), C(3, 1) Image A'B'C':A'(1, 3), B'(2, 1), C'(3, 1) Reflection across the x-axis; congruent Lesson Quiz Identify each transformation from the original to the image, and tell whether the two figures are similar or congruent. 1. Original ABC: A(-4, -2), B(-3, 1), C(-2, -2) Image ABC: A'(2, 1), B'(3, 4), C'(4, 1) 2. Original: A(2, 1), B(2, 3), C(4, 3), D(4, 1) Image ABCD: A'(4, 2), B'(4, 6), C '(8, 6), D'(8, 2)