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geometry similarity

Postulates and theorems for proportions and similarity (chp. 6)

HypothesisConclusion
If the two angles of one triangle are congruent to two angles of another triangle then the triangles are similar
If the measures of the corresponding sides of two triangles are proportional then the triangles are similar
If the measures of two sides of a triangle are proportional to the measures of two corresponding sides of another triangle and the included angles are congruent then the triangles are similar
Similarity of triangles is reflexive, symmetric, and transitive
If a line is parrallel to one side of a triangle and intersects the other two sides in two distinct points then it seperates these sides into segments of proportional lengths
If a line intersects two sides of a triangle and seperates the sides into corresponding segments of proportional lengths then the line is parrallel to the third side
A midsegment of a triangle is parrallel to one side of the triangle its length is one-half the length of that side
If three or more parallel lines intersect two transversals then they cut off the transversasl proportionally
If three or more parallel lines cut off congruent segments on one transversal then they cut off congruent segments on every transversal
If two triangles are similar then the perimeters are proportional to the measures of corresponding sides
If two triangles are similar then the measures of the corresponding altitudes are proportional to the measures of the corresponding sides
If two triangles are similar then the measures of the corresponding angle bisectors of the triangles are proportional to the measures of the corresponding sides
If two triangles are similar then the measures of the corresponding medians are proportional to the measures of the corresponding sides
An angle bisector in a triangle seperates the opposite side into segments that have the same ratio as the other two sides
Created by: m.meyer