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Angle-Angle Similarity
If the 2 angles in one triangle are congruent to 2 angles of another triangle, then the triangles are similar
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Side-Side-Side Similarity
If the measures of the corresponding sides of two triangles are proportional, then the triangles are similar.
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Side-Angle-Side Similarity
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.
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Triangle Proportionality Theorem
If a line is parallel to one side of a triangle and intersects the other sides in two distinct points, then it separates these sides into segments of proportional lengths.
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Triangle Midsegment Theorem
A midsegment of a triangle is parallel to one side of the triangle, and its length is one-half the length of that side.
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Corallaries
If three or more parallel lines intersect two transversals, then they cut off the transversals proportionally.
If three or more parallel lines cut off congruent segments on one transversal, then they cut off congruent segments on every transversal.
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Proportional Perimiters Theorem
If two triangles are similar, then the perimeters are proportional to the measures of the corresponding sides.
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Altitudes
If two triangles are similar, then the corresponding altitudes are proportional to the measures of the corresponding sides.
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Angle Bisectors
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.
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Medians
If two triangles are similar, then the measures of the corresponding medians are proportional to the measure of the corresponding sides.
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Angle Bisector Theorem
An angle bisector in a triangle separates the opposite side to segments that have the same ratio as the other two sides.
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