## Geometry Chapter 7 Theorems

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fissmoss  on April 1, 2010

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# Geometry Chapter 7 Theorems

 Theorem 7.1 Perimeters of Similar PolygonsIf two polygons are similar, then their perimeters are proportional to the scale factor between them.
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#### Definitions

Theorem 7.1 Perimeters of Similar Polygons If two polygons are similar, then their perimeters are proportional to the scale factor between them.
Postulate 7.1 Angle-Angle (AA) Similarity If two angles of one triangle are congruent to two angles of another triangle, then the triangles are similar.
Theorem 7.2 Side-Side-Side (SSS) Similarity IF the corresponding side lengths of two triangles are proportional, then the triangles are similar.
Theorem 7.3 Side-Angle-Side (SAS) Similarity If the lengths of two sides of one triangle are proportional to the lengths of two corresponding sides of another triangle and the included angles are congruent, then the triangles are similar.
Theorem 7.5 Triangle Proportionality Theorem If a line is parallel to one side of a triangle and intersects the other two sides, then it divides the sides into segments of proportional lengths.
Theorem 7.6 Converse of Triangle Proportionality Theorem If a line intersects two sides of a triangle and separates the sides into proportional corresponding segments, then the line is parallel to the third side of the triangle.
Theorem 7.7 Triangle Midsegment Theorem A midsegment of a triangle is parallel to one side of the triangle, and its length is one half of the length of that side.
Corollary 7.1 Proportional Parts of Parallel Lines If three or more parallel lines intersect two transversals, then they cut off the transversals proporotionally
Corollary 7.2 Congruent Parts of Parallel Lines If three or more parallel lines cut off congruent segments on one transversal, then they cut off congruent segments on every transversal.
Theorem 7.8 Altitudes If two triangles are similar, the lengths of corresponding altitudes are proportional to the lengths of corresponding sides.
Theorem 7.9 Angle Bisectors If two triangles are similar, the lengths of corresponding angle bisectors are proportional to the lengths of corresponding sides.
Theorem 7.9 Medians If two triangles are similar, the lengths of corresponding medians are proportional to the lengths of corresponding sides.
Theorem 7.11 Triangle Angle Bisector An angle bisector in a triangle separates the opposite side into two segments that are proportional to the lengths of the other two sides.

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