1. Warm Up
Problem of the Day
Lesson Presentation
Lesson Quizzes

2. Warm Up
Graph the polygons with the given vertices. Identify the most specific name for each polygon.
1. A(2, 1), B(-1, 3), C(5, 3)
obtuse isosceles triangle
2. A(-4, -3), B(-2, 1), C(3, 1),D(1, -3)
parallelogram

3. Problem of the Day
ABC DEF. The length of BC is 3k and the length of EF is 54.
Find k. 18

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

5. Vocabulary
Similarity transformations
Congruence transformations

6. 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 as the original, but a different size are similarity transformations.

7. Transformations that result in an image that is the same shape and the same size as the original are congruence transformations.

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

9. 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.

10. 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.

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

12. 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

13. 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

14. 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

15. 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

16. Lesson Quiz for Student Response Systems
Lesson Quizzes
Standard Lesson Quiz
Lesson Quiz for Student Response Systems 16

17. 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)
Translation right 6 units and up 3 units; congruent

18. Lesson Quiz Continued
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)
Dilation by a factor of 2; similar

19. Lesson Quiz for Student Response Systems
Identify each transformation from the original to the image, and tell whether the two figures are similar or congruent.
1. Original ABCD: A(1, –2), B(2, –2), C(2, –1),
D(1, –1)
Image A'B'C'D': A'(2, –4), B’(4, –4), C'(4, –2),
D'(2, –2)
A. Translation 2 units down; congruent
B. Translation 2 units down; similar
C. Dilation by a factor of 2; congruent
D. Dilation by a factor of 2; similar

20. Continued: Lesson Quiz for Student Response Systems
Identify each transformation from the original to the image, and tell whether the two figures are similar or congruent.
2. Original ABC : A(–1, –3), B(–2, 1), C(3, –1)
Image A'B'C‘ : A'(1, 0), B'(0, 4), C'(5, 2)
A. Translation right 2 units and up 3 units; congruent
B. Translation left 2 units and down 3 units; similar
C. Translation right 2 units and up 3 units; similar
D. Translation left 2 units and down 3 units; congruent