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Geometry: Similarity Vocabulary
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Terms in this set (20)
Angle-Angle Similarity Postulate (AA~ Post.)
If two angles of one triangle are congruent to two angles of another triangle, then the triangles are similar.
Side-Side-Side Similarity Theorem (SSS~ Thm. )
If the three sides of one triangle are proportional to the three corresponding sides of another triangle, then the triangles are similar
Side-Angle-Side Similarity Theorem (SAS~ Thm. )
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 (Δ Proportionality Thm.)
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 (Conv. of Δ Proportionality Thm.)
If a line divides two sides of a triangle proportionally, then it is parallel to the third side
Two-Transversal Proportionality Corollary (2-Transv. Proportionality Cor.)
If three or more parallel lines intersect two transversals, then they divide the transversals proportionally.
Triangle Angle Bisector Theorem (Δ∠ Bisector Thm.)
An angle bisector of a triangle divides the opposite side 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, or (a/b)^2.
Ratio
compares two numbers by division
Extremes
In the proportion a/b=c/d, a and d are the _
Means
In the proportion a/b=c/d, b and c are the _
Similar Polygons
Two polygons are ____________ if and only if their corresponding angles are congruent and their corresponding side lengths are proportional
Reflexive property of similarity
ΔABC~ΔABC
Symmetric Property of Similarity
If ΔABC ~ ΔDEF, then ΔDEF~ΔABC
Transitive Property of Similarity
If ΔABC~ ΔDEF and ΔDEF~ΔXYZ, then ΔABC~ΔXYZ
Indirect measurement
Any method that uses formulas, similar figures, and/or proportions to measure and object
Scale drawing
Represents an object as smaller than or larger than its actual size
Scale
Ratio of any length in 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 enlarged or reduced
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