Lesson 7 – 6 Similarity Transformations

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Presentation transcript:

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

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.

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

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

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

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.

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

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

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…

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

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

Homework Pg. 508 1 – 5 all, 6 – 14 E, 18, 28 – 44 E