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Similar Triangles

TermDefinition
Angle-Angle Similarity Postulate This (AA) is one of the three ways to test that two triangles are similar. Triangles are similar if the measure of two interior angles in one triangle are the same as the corresponding angles in the other.
Side-Side-Side Similarity Postulate This (SSS) is one of the three ways to test that two triangles are similar. Triangles are similar if all three sides in one triangle are in the same proportion to the corresponding sides in the other.
Side-Angle-Side Similarity Postulate This (SAS) is one of the three ways to test that two triangles are similar. Triangles are similar if two sides in one triangle are in the same proportion to the corresponding sides in the other, and the included angle are equal.
Ratio The relationship between two measures, expressed as the number of times one is bigger or smaller than the other.
Extended Ratio An extended ratio compares more that two quantities and is expressed in a form a : b : c : d.
Proportion An equation that states that two ratios are equal.
Cross Product Property The means-extremes property of proportions allows you to cross multiply, taking the product of the means and setting them equal to the product of the extremes. This property comes in handy when you're trying to solve a proportion.
Similar Triangles Triangles are similar if they have the same shape, but not necessarily the same size. Corresponding angles are congruent (same measure) Corresponding sides are all in the same proportion.
Scale Factor The ratio of any two corresponding lengths in two similar geometric figures.
Triangle Proportionality Theorem a line drawn parallel to any of the sides of a triangle divides the other two sides proportionally.
Triangle Midsegment Theorem In a triangle, the segment joining the midpoints of any two sides will be parallel to the third side and half its length.
Proportional Parts of Parallel Lines If 3 or more parallel lines intersect two transversals, then they divide those transversals proportionally.
Special Segments of Similar Triangles - Altitudes If two triangles are similar, the lengths of corresponding altitudes are proportional to the lengths of corresponding sides.
Triangle Angle Bisector An angle bisector of an angle of a triangle divides the opposite side in two segments that are proportional to the other two sides of the triangle.
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.
Special Segments of Similar Triangles - Angle Bisectors If two triangles are similar, the lengths of corresponding angle bisectors are proportional to the lengths of corresponding sides.
Special Segments of Similar Triangles - Medians If two triangles are similar, the lengths of corresponding medians are proportional to the lengths of corresponding sides.
Created by: jilltrahan