1. Learn to identify transformations as similarity or congruence transformations.

2. Vocabulary
Similarity transformations
Congruence transformations

3. 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.

4. *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.

5. A dilation produces an image that is similar to the original.
Remember!

6. 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.

7. 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.

8. Helpful Hint Rotations, translations, and reflections do not
change the size or shape of a figure.
Helpful Hint

9. 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

10. 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

11. 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

12. 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

13. 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)