Similarity and Congruence Transformations5-7

Warm UpWarm Up

Lesson PresentationLesson Presentation

Problem of the DayProblem of the Day

Lesson QuizzesLesson Quizzes

Similarity and Congruence Transformations5-7

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

Similarity and Congruence Transformations5-7

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

18

Similarity and Congruence Transformations5-7

Learn to identify transformations as similarity or congruence transformations.

Similarity and Congruence Transformations5-7

Similarity transformationsCongruence transformations

Vocabulary

Similarity and Congruence Transformations5-7

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.

Similarity and Congruence Transformations5-7

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

Similarity and Congruence Transformations5-7

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

Remember!

Similarity and Congruence Transformations5-7Additional Example 1: Identifying Similarity

TransformationsIdentify 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.

Similarity and Congruence Transformations5-7

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.

Similarity and Congruence Transformations5-7

Rotations, translations, and reflections do notchange the size or shape of a figure.

Helpful Hint

Similarity and Congruence Transformations5-7Additional 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

Similarity and Congruence Transformations5-7

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

Similarity and Congruence Transformations5-7

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

Additional Example 2: Continued

Similarity and Congruence Transformations5-7Check 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

Similarity and Congruence Transformations5-7

Lesson Quizzes

Lesson Quiz for Student Response Systems

Standard Lesson Quiz

Similarity and Congruence Transformations5-7

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

Similarity and Congruence Transformations5-7

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

Similarity and Congruence Transformations5-7

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; congruentB. Translation 2 units down; similarC. Dilation by a factor of 2; congruentD. Dilation by a factor of 2; similar

Similarity and Congruence Transformations5-7

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; congruentB. Translation left 2 units and down 3 units; similarC. Translation right 2 units and up 3 units; similarD. Translation left 2 units and down 3 units; congruent

Continued: Lesson Quiz for Student Response Systems