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geometry similarity
Postulates and theorems for proportions and similarity (chp. 6)
Hypothesis | Conclusion |
---|---|
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 |