Defining Similarity (5.3.1)

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Presentation transcript:

Defining Similarity (5.3.1) April 18th, 2015

Similar Figures Have the same shape, but different sizes and position. Have corresponding angles that are congruent. Have corresponding side lengths that are proportional, or have a constant ratio (called the ratio of similitude or scale factor). means “triangle ABC is similar to triangle DEF.

since and

Similarity Transformations The combination of a rigid motion (reflection, rotation, or translation) with a dilation is called a similarity transformation. You can prove two figures are similar by finding a similarity transformation that maps one figure onto the other.

2) Then translate point D onto point A. 1) Start with a dilation of with center A and scale factor 2. Since dilations preserve angle measure, Finally, reflect over line n to map onto . Since translations and reflections preserve angle measure and side length, and .

Ex. 1: Find the angle measures and side lengths for each triangle, given that *The angle measures in a triangle add to .

*To see if two triangles are similar, first investigate if the corresponding angle measures are congruent. If they are, check to see if you can use a similarity transformation to map one triangle onto the other.