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WHS Ch 7 Similarity

WHS Chapter 7 Similarity

side of a polygon one of the segments that form a polygon
denominator the bottom number of a fraction, which tells how many equal parts are in the whole
numerator the top number of a fraction, which tells how many parts of a whole are being considered
vertex of a polygon the intersection of two sides of a polygon
vertical angles two nonadjacent angles formed by two intersecting lines
dilation a transformation I which the lines connecting every point P with its preimage P' all intersect at a point C known as the center of dilation; a transformation that changes the size of a figure but not the shape
scale ratio between two corresponding measurements
scale drawing drawing that uses a scale to represent an object as smaller or larger than the actual object
scale factor multiplier used on each dimension to change one figure into a similar figure
similar two figures have the same shape but not necessarily the same size
similar polygons two polygons whose corresponding angles are congruent and whose corresponding side lengths are proportional
similarity ratio ratio of two corresponding linear measurements in a pair of similar figures
similarity transformation a dilation or a composite of one or more dilations and one or more congruence transformations
reduction the scale factor k in a dilation is a value between 0 and 1
AA Similarity Postulate If two angles of one triangle are congruent to two angels of another triangle, then the triangles are similar
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.
SAS Similarity Theorem If two sides of one triangle are proportional to two sides of another triangle and their included angels are congruent, then the triangles are similar
Reflexive Property of Similarity ∆ ABC ~ ∆ ABC
Symmetric Property of Similarity If ∆ ABC ~ ∆ DEF, then ∆ DEF ~ ∆ ABC.
Transitive Property of Similarity If ∆ ABC ~ ∆ DEF and ∆ DEF ~ ∆ XYZ, then ∆ ABC ~ ∆ XYZ.
Triangle Proportionality Theorem If a line parallel to a side of a triangle intersects the other two sides, then it divides those sides proportionally.
indirect measurement any method that uses formulas, similar figures, and/or proportions to measure an object
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 or (a:b)².
Created by: cawhite