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Warm Up Problem of the Day Lesson Presentation Lesson Quizzes

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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

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

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

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Vocabulary Similarity transformations Congruence transformations

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**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.

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

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**A dilation produces an image that is similar to the original.**

Remember!

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**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.

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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.

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**Helpful Hint Rotations, translations, and reflections do not**

change the size or shape of a figure. Helpful Hint

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**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

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**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

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**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

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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

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**Lesson Quiz for Student Response Systems**

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

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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

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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

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**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

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**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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