Holt McDougal Geometry 7-2 Similarity and Transformations 7-2 Similarity and Transformations Holt GeometryHolt McDougal Geometry

7-2 Similarity and Transformations Warm Up Find the image point when the indicated transformation is applied to the given pre-image point. 1. (x, y) → (x + 3, y – 1); (2, 4) 2. (x, y) → (x, –y); (–2, 1) 3. (x, y) → (3x, 3y); (–5, 0) 4. (x, y) → ; (3, -6) 3 1 x, 3 1 y

Holt McDougal Geometry 7-2 Similarity and Transformations A transformation that produces similar figures is a similarity transformation. A similarity transformation is a dilation or a composite of one or more dilations and one or more congruence transformations. Two figures are similar if and only if there is a similarity transformation that maps one figure to the other figure. The scale factor describes how the figure is enlarged or reduced.

Holt McDougal Geometry 7-2 Similarity and Transformations Translations, reflections, and rotations are congruence transformations. Dilations are similarity transformations. Remember!

Holt McDougal Geometry 7-2 Similarity and Transformations D: (x, y) → (3x, 3y) A(1, 1), B(3, 1), C(3, 2) A. Apply the dilation D to the polygon with the given vertices. Describe the dilation.

Holt McDougal Geometry 7-2 Similarity and Transformations Apply the dilation D : (x, y) → polygon with vertices D(-8, 0), E(-8, -4), and F(-4, -8). Name the coordinates of the image points. Describe the dilation. to the 4 1 x, 4 1 y

Holt McDougal Geometry 7-2 Similarity and Transformations A.A(–6, -6), B(-6, 3), C(3, 3), D(3, -6) and H(-2, -2), J(-2, 1), K(1, 1), L(1, -2) Determine whether the polygons with the given vertices are similar. If so, give the rule.

Holt McDougal Geometry 7-2 Similarity and Transformations B. P(2, 0), Q(2, 4), R(4, 4), S(4, 0) and W(5, 0), X(5, 10), Y(8, 10), Z(8, 0).

Holt McDougal Geometry 7-2 Similarity and Transformations Explore dilations further CharacteristicsOriginal Triangle ABC New Triangle A’B’C’ Observations CoordinatesA(3,5) B(3,2) C(7,2) Angle Measures 53 ᵒ - 90ᵒ - 37ᵒ Length of Sides Perimeter Area Record observations using a scale factor of 2.

Holt McDougal Geometry 7-2 Similarity and Transformations CharacteristicsOriginal Rectangle ABCD New Rectangle A’B’C’D’ Observations CoordinatesA(-2,4), B(-2,-2), C(4,-2), D (4,4) Angle Measures 90 ᵒ - 90ᵒ -90ᵒ - 90ᵒ Length of Sides Perimeter Area Record observations using a scale factor of 1/2. Explore dilations further

Holt McDougal Geometry 7-2 Similarity and Transformations

Holt McDougal Geometry 7-2 Similarity and Transformations A. Circle A with center (0, 0) and radius 1 is similar to circle B with center (0, 6) and radius 3.

Holt McDougal Geometry 7-2 Similarity and Transformations B. Circle C with center (0, –3) and radius 2 is similar to circle D with center (5, 1) and radius 5.

Holt McDougal Geometry 7-2 Similarity and Transformations Prove that circle A with center (2, 1) and radius 4 is similar to circle B with center (-1, -1) and radius 2.

Holt McDougal Geometry 7-2 Similarity and Transformations CharacteristicsOriginal Circle with diameter AB New circle with diameter A’B’ Observations CoordinatesA(4,1) B(4,-3) Length of diameter4 cm Length of radius Circumference Area Record observations using a scale factor of 2 Explore dilations further

Holt McDougal Geometry 7-2 Similarity and Transformations 1. Apply the dilation D: (x, y) to the polygon with vertices A(2, 4), B(2, 6), and C(6, 4). Name the coordinates of the image points. Describe the dilation.

Holt McDougal Geometry 7-2 Similarity and Transformations Determine whether the polygons with the given vertices are similar. 2. A(-4, 4), B(6, 4), C(6, -4), D(-4, -4) and P(-2, 2), Q(4, 2), R(4, -2), S(-2, -2)

Holt McDougal Geometry 7-2 Similarity and Transformations 3. Prove that circle A with center (0, 4) and radius 4 is similar to circle B with center (-2, -7) and radius 6.