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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 & PostulatesAngle-Angle (AA) Similarity Postulate | If two angles of one triangle are congruent to two angles of another triangle, then the triangles are similar | Side-Side-Side (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 | Aide-Angle-Side (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 | Two-Transversal 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 a2/b2 |
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