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Geometry Unit 7 Cheat Sheet by

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
           
 

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