WHS Chapter 7 Similarity
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each of the black spaces below before clicking
on it to display the answer.
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| side of a polygon | one of the segments that form a polygon
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| denominator | the bottom number of a fraction, which tells how many equal parts are in the whole
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| numerator | the top number of a fraction, which tells how many parts of a whole are being considered
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| vertex of a polygon | the intersection of two sides of a polygon
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| vertical angles | two nonadjacent angles formed by two intersecting lines
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| 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
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| scale | ratio between two corresponding measurements
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| scale drawing | drawing that uses a scale to represent an object as smaller or larger than the actual object
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| scale factor | multiplier used on each dimension to change one figure into a similar figure
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| similar | two figures have the same shape but not necessarily the same size
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| similar polygons | two polygons whose corresponding angles are congruent and whose corresponding side lengths are proportional
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| similarity ratio | ratio of two corresponding linear measurements in a pair of similar figures
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| similarity transformation | a dilation or a composite of one or more dilations and one or more congruence transformations
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| reduction | the scale factor k in a dilation is a value between 0 and 1
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| AA Similarity Postulate | If two angles of one triangle are congruent to two angels of another triangle, then the triangles are similar
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| 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.
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| 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
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| Reflexive Property of Similarity | ∆ ABC ~ ∆ ABC
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| Symmetric Property of Similarity | If ∆ ABC ~ ∆ DEF, then ∆ DEF ~ ∆ ABC.
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| Transitive Property of Similarity | If ∆ ABC ~ ∆ DEF and ∆ DEF ~ ∆ XYZ, then ∆ ABC ~ ∆ XYZ.
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| Triangle Proportionality Theorem | If a line parallel to a side of a triangle intersects the other two sides, then it divides those sides proportionally.
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| indirect measurement | any method that uses formulas, similar figures, and/or proportions to measure an object
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| 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.
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