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SimilarityConclusionSimilarity ConclusionMATH 113Section 9.2: SimilarityProf. Jonathan DuncanWalla Walla CollegeWinter Quarter, 2007Similarity ConclusionSimilarity and CongruenceAs you have no doubt noted by now, terminology is very important inGeometry. When we say to shapes are equal, that has a very precisemeaning. In the same way, when we say two shapes are similar, we meansomething specific.SimilarityTwo polygons are similar if and only if all corresponding angles arecongruent and corresp onding sides are proportional.ExampleHow does the definition above differ from the definition of congruentpolygons?ExampleIf two polygons are similar, are they congruent?If two polygons are congruent, are they always similar?Similarity ConclusionExploring a Pair of Similar FiguresTo help us better understand similarity, consider this example.ExampleGive a justification for the claim that the two rectangles below aresimilar.10 units20 units8 units4 unitsABC DWZYXSimilarity ConclusionSimilarity TransformationsAt the beginning of chapter 9, we talked about several differenttypes of transformations. Which of these are similaritytransformations?Types of TransformationsName What Changes What Doesn’tTranslation Position Size, Shape, OrientationReflectionPosition, Orientation Size, ShapeRotation Position, Orientation Size, ShapeShrink/Grow Position, Size Shape, OrientationDistortionPosition, Size, Shape NeighborhoodsSimilarity TransformationsAll types but the last, distortions, are similarity transformations.Similarity ConclusionSimilarity and PerspectiveAnother way to think of similarity is as an enlargement or reduction of animage along lines of perspective.Similarity Along Lines of PerspectiveThe following p olygon has been enlarged by extending perspective linesfrom a single point through each vertex.ExampleA triangle has vertices A(1, 4), B (3, 2) and C (1, 1). Draw a similartriangle by multiplying each coordinate by 3. Sketch the perspective linesfor these similar figures.Similarity ConclusionImportant ConceptsThings to Remember from Section 9.31Definition of similarity for polygons2Similarity transformations3Sketching similar figures using lines of


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