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Warm Up

Learn to identify similarity and congruence transformations in art & design using geometric shapes. Practice identifying transformations from original to image and determining similarity or congruence. Homework and quizzes included.

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Warm Up

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

  2. Math Journal (5 Min) • Vocabulary – Each student will be given vocabulary words that are found within the lesson. They must then, at the beginning of class, write what they think the definitions before they have been taught the lesson and, at the end of class, write about what they now know the definitions are after they have been taught the lesson. Then, each student will discuss his/her answers within their group. Finally, to leave class, each student will have to give/write 1 word and definition that pertained to the lesson.

  3. Homework Review (5 Min)

  4. 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

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

  6. Textbook Examples (I Do) (5 Min)

  7. Learnto identify transformations as similarity or congruence transformations.

  8. Vocabulary Similarity transformations Congruence transformations

  9. 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.

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

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

  12. 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.

  13. 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.

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

  15. 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

  16. 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

  17. 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

  18. 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

  19. Class work Problems (We Do) (10 Min) • Pg. 233-235 (1-8)

  20. Small Group CW(Yall Do) (10 Min) • Pg. 233-235 (10-28 EOE)

  21. Homework (You Do) (10 Min) • Pg. 233-235 (9, 11, 15, 19, 21 odd)

  22. Math Journal (5 Min) • Vocabulary – Each student will be given vocabulary words that are found within the lesson. They must then, at the beginning of class, write what they think the definitions before they have been taught the lesson and, at the end of class, write about what they now know the definitions are after they have been taught the lesson. Then, each student will discuss his/her answers within their group. Finally, to leave class, each student will have to give/write 1 word and definition that pertained to the lesson.

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

  24. 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

  25. 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

  26. 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

  27. 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

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