Holt McDougal Geometry
7-2 Similarity and Transformations7-2 Similarity and Transformations
Holt GeometryHolt McDougal Geometry
Holt 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) 31 x,
31 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 41 x,
41 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
Characteristics Original Triangle ABC
New Triangle A’B’C’
Observations
Coordinates A(3,5) B(3,2) C(7,2)
Angle Measures 53ᵒ - 90ᵒ - 37ᵒ
Length of Sides
Perimeter
Area
Record observations using a scale factor of 2.
Holt McDougal Geometry
7-2 Similarity and Transformations
Characteristics Original Rectangle ABCD
New Rectangle A’B’C’D’
Observations
Coordinates A(-2,4), B(-2,-2), C(4,-2), D (4,4)
Angle Measures 90ᵒ - 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
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
Characteristics Original Circle with diameter AB
New circle with diameter A’B’
Observations
Coordinates A(4,1) B(4,-3)
Length of diameter 4 cm
Length of radius
Circumference
Area
Record observations using a scale factor of 2Explore 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)