Warm Up Problem of the Day Lesson Presentation Lesson Quizzes

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

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

Learn to identify transformations as similarity or congruence transformations.

Vocabulary Similarity transformations Congruence transformations

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.

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

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

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.

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.

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

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

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

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

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

Lesson Quiz for Student Response Systems 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

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

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

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