Vocabulary Similarity transformations Congruence transformations

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Vocabulary Similarity transformations Congruence transformations

Text of 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)