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Holt McDougal Geometry Unit 7
VocabularySimilar Polygons  Two polygons are similar polygons if and only if their corresponding angles are congruent and their corresponding side lengths are proportional  Similarity Ratio  The ratio of the lengths of the corresponding sides of two similar polygons  Similarity Transformation  A dilation or a composite of one or more dilations and one or more congruence transformations  Dilation  (kx, ky)  Indirect Measurement  Any method of measuring that uses formulas, similar figures, and/or proportions to measure an object  Scale Drawing  Represents an object as smaller or larger than its actual size  Scale  The ratio of any length in the drawing to the corresponding actual length  Dilation  A transformation that changes the size of a figure but not its shape  Scale Factor  Describes how much the figure is enlarge or reduced 
  Similar ShapesAll circles and squares are similar because they all have the same shape. 
Properties of SimilarityReflexive  Triangle ABC is similar to triangle ABC  Symmetric  If triangles ABC is similar to DEF, then triangle DEF is similar to triangle ABC  Transitive  If triangle ABC is similar to DEF and triangle DEF is similar to XYZ, then triangle ABC is similar to triangle XYZ 
  Theorems & PostulatesAngleAngle (AA) Similarity Postulate  If two angles of one triangle are congruent to two angles of another triangle, then the triangles are similar  SideSideSide (SSS) Similarity Theorem  If the three sides of one triangle are proportional to the three corresponding sides of another triangle, then the triangles are similar  AideAngleSide (SAS) Similarity  If two sides of one triangle are proportional to two sides of another triangle and their included angles are congruent, then the triangles are similar  Triangle Proportionality Theorem  If a line parallel to a side of a triangle intersects the other two sides, then it divides those sides proportionally  Converse of the Triangle Proportionality Theorem  If a line divides two sides of a triangle proportionally, then it is parallel to the third side  TwoTransversal Proportionality  If three or more parallel lines intersect two transversals, then they divide the transversals proportionally  Triangle Angle Bisector Theorem  An angle bisector of a triangle divides the opposite sides into two segments whose lengths are proportional to the lengths of the other two sides  Proportional Perimeters and Areas Theorem  If the similarity ratio of two similar figures is a/b, then the ratio of their perimeters is a/b, and the ratio of their areas is a^{2}/b^{2} 

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