[PDF] 7-6 Study Guide and Intervention - Similarity Transformations





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7-6 - Study Guide and Intervention

Glencoe Geometry. 7-6. Identify Similarity Transformations A dilation is a transformation that enlarges or reduces the original figure proportionally.



7-6 Study Guide and Intervention - Similarity Transformations

Chapter 7. 37. Glencoe Geometry. 7-6 Study Guide and Intervention. Similarity Transformations. Identify Similarity Transformations A dilation is a 



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NAME _____________________________________________ DATE ____________________________ PERIOD _____________

Chapter 7 37 Glencoe Geometry

7-6 Study Guide and Intervention

Similarity Transformations

Identify Similarity Transformations A dilation is a transformation that enlarges or reduces the original figure

proportionally. The scale factor of a dilation, k, is the ratio of a length on the image to a corresponding length on the

preimage. A dilation with k > 1 is an enlargement. A dilation with 0 < k < 1 is a reduction.

Example: Determine whether the dilation from A to B is an enlargement or a reduction. Then find the scale factor

of the dilation. a. b. B is larger than A, so the dilation is an enlargement. The distance between the vertices at (3, 4) and (1, 4) for A is 2. The distance between the vertices at (0, 3) and (4, 3) for B is 4.

The scale factor is ସ

6 or 2.

B is smaller than A, so the dilation is a reduction. The distance between the vertices at (2, 3) and (2, 3) for A is 6. The distance between the vertices at (2, 1) and (2, 2) for B is 3.

The scale factor is ଷ

: or ଵ 6

Exercises

Determine whether the dilation from A to B is an enlargement or a reduction.

Then find the scale factor of the dilation.

1. 2.

3. 4.

reduction; ૝

NAME _____________________________________________ DATE ____________________________ PERIOD _____________

Chapter 7 38 Glencoe Geometry

7-6 Study Guide and Intervention (continued)

Similarity Transformations

Verify Similarity You can verify that a dilation produces a similar figure by comparing all corresponding sides and

angles. For triangles, you can also use SAS Similarity.

Example: Graph the original figure and its dilated image. Then verify that the dilation is a similarity

transformation. a. original: A(3, 4), B(2, 4), C(3, 4) image: D(1, 0),

E(3.5, 0), F(1, 4)

Graph each figure. Since סA and ס

angles, סA ס ؆ that include סA and ס similarity by SAS. Use the coordinate grid to find the lengths of vertical segments AC and DF and horizontal segments

AB and DE.

8 = 2 and ஺஻

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