1. Lesson 7 – 6 Similarity Transformations
Geometry
Lesson 7 – 6
Similarity Transformations
Objective:
Identify similarity transformations.
Verify similarity after a similarity transformation.

2. Dilation Dilation Similarity Transformation Center of Dilation
A transformation that enlarges or reduces the original figure proportionally.
Similarity Transformation
A transformation that results in similar figures.
Center of Dilation
Dilations are performed with respect to a fixed point.

3. Scale Factor Scale factor of a dilation
The ratio of a length on the image to a corresponding length on the preimage

4. Types of Dilations
Enlargement
A dilation with a scale factor of 1

5. Types of Dilation Reduction
A dilation with a scale factor between 0 and 1

6. Reduction Enlargement Scale factor: 3/6 = 1/2 Scale factor: 4/3
Determine whether the dilation from A to B is an enlargement or a reduction. Then find the scale factor of the dilation.
Reduction
Enlargement
Scale factor: 3/6 = 1/2
Scale factor: 4/3
*Note scale factor is ½
and not 2 since it is a
reduction.

7. Enlargement Reduction Scale factor: 5/4 Scale factor: 1/3
Determine whether the dilation from A to B is an enlargement or a reduction. Then find the scale factor of the dilation.
Enlargement
Reduction
Scale factor: 5/4
Scale factor: 1/3

8. Graph the original figure and its dilated image
Graph the original figure and its dilated image. Then verify that the dilation is a similarity transformation.
Original: A (-6, -3), B (3, 3) C (3, -3)
Image: X (-4, -2), Y (2, 2), Z (2, -2)
Angles Z & C are right angles.
Does SAS similarity work?
ABC ~ XYZ by SAS Similarity

9. Original: J(-6, 4) K (6,8) L(8,2) M(-4,-2)
Graph the original figure and its dilated image. Then verify that the dilation is a similarity transformation.
Original: J(-6, 4) K (6,8) L(8,2) M(-4,-2)
Image: P (-3,2) Q (3,4) R (4, 1) S (-2, -1)
We need to check to see if all
sides are proportional
Cont…

10. The sides are proportional. Cont…
Set up the ratios, the dilation is a reduction so smaller on top.
The sides are
proportional.
Cont…

11. The sides are proportional, but no you have to check
that the angles are congruent.
Diagonals are congruent so the figures are rectangles.
The sides are proportional and the angles are congruent
So therefore PQRS ~ JKLM

12. Homework
Pg – 5 all, 6 – 14 E, 18, 28 – 44 E