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) 90º 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 A’B’C’: A'(2, 1), B'(3, 4), C'(4, 1) 2. Original: A(2, 1), B(2, 3), C(4, 3), D(4, 1) Image A’B’C’D’: A'(4, 2), B'(4, 6), C '(8, 6), D'(8, 2)