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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 |
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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 |
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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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