Cheatography

# Geometry Unit 7 Cheat Sheet by CCRoses

Holt McDougal Geometry Unit 7

### Vocabulary

 Similar 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 Shapes

 All circles and squares are similar because they all have the same shape.

### Properties of Similarity

 Reflexive 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 & Postulates

 Angle-­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