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WHS Ch 7 Similarity
WHS Chapter 7 Similarity
| Term | Definition |
|---|---|
| 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
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