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Identify Polygon Transformations

Learn how to identify similarity and congruence transformations of polygons by graphing their vertices and analyzing their size and shape.

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Identify Polygon Transformations

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  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. Objective- to identify transformations as similarity or congruence transformations.

  4. Vocabulary Similarity transformations Congruence transformations

  5. 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.

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

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

  8. 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.

  9. 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.

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

  11. 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

  12. 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

  13. 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

  14. 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

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

  16. 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

  17. 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

  18. 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

  19. 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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