1. Similarity and Transformations
7-2
Similarity and Transformations
Holt Geometry
Warm Up
Lesson Presentation
Lesson Quiz
Holt McDougal Geometry

2. 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)
(5, 3)
2. (x, y) → (x, –y); (–2, 1)
(-2,-1)
3. (x, y) → (3x, 3y); (–5, 0)
(-15,0) 3 1 x, y
4. (x, y) →
; (3, -6)
(1,-2)

3. Objectives
Draw and describe similarity transformations in the coordinate plane.
Use properties of similarity transformations to determine whether polygons are similar and to prove circles similar.

4. Vocabulary
similarity transformation

5. 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.

6. Congruence transformations are different from similarity
Translations, reflections, and rotations are congruence transformations.
Remember!
Congruence transformations are different from similarity
transformations because….
Angles and sides are exactly the same measurements
when dealing with congruent triangles
In similar triangles the angles are exactly the same measurements
The sides are PROPORTIONAL (ratio/fractions must be simplified)
Dilation is the ONLY transformation that is SIMILAR polygons

7. Example 1: Drawing and Describing Dilations
A. Apply the dilation D to the polygon with the given vertices. Describe the dilation.
D: (x, y) → (3x, 3y) A(1, 1), B(3, 1), C(3, 2)
Dilation (enlargement) with center (0, 0) and scale factor 3

8. Example 1: Continued
B. Apply the dilation D to the polygon with the given vertices. Describe the dilation.
D: (x, y) →
P(–8, 4), Q(–4, 8), R(4, 4) 4 3 x, y

9. Check It Out! Example 1
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, y
D'(-2, 0), E'(-2, -1), F'(-1, -2); dilation with center
(0, 0) and scale factor 1 4
Reduction

10. Example 2 : Determining Whether Polygons are Similar
Determine whether the polygons with the given vertices are similar.
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)
Yes; ABCD maps to HJKL by a dilation:
(x, y) → 1 3 x y ,
Reduction

11. On your Own : Part-I
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.
A’(3, 6), B’(3, 9), C’(9, 6); dilation with center
(0, 0) and scale factor 3 2
Enlargement

12. On your Own : Part-I
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)
No; (x, y) → (0.5x, 0.5y) maps A to P, but not B to Q.
3. A(2, 2), B(2, 4), C(6, 4) and
D(3, -3), E(3, -6), F(9, -6)
Yes; △ ABC maps to △ A’B’C’ by a reflection: (x, y) → (x, -y). Then △ A’B’C’ maps to △DEF by a dilation:(x, y) → (1.5x, 1.5y).