Similar Triangles

Postulate: The AA Similarity Postulate:

If two angles of a triangle are congruent with two angles of another triangle then the triangles are similar.

Theorem: The SAS Similarity Theorem:

If an angle of a triangle is congruent with another angle of a different triangle and their sides including the angles are in proportion then, the triangles are similar.

Theorem: The SSS Similarity Theorem:

If the sides of a two triangles are in proportion then, the triangles are similar.

Theorem: Triangle Proportionality Theorem:

If a line parallel to one of the sides of a triangle intersects the other two sides then, the line divides those sides proportionally.

Corollary:

If three parallel lines intersect two transversals then, the parallel lines divide the transversal proportionally.

Theorem: The Triangle Angle-Bisector Theorem:

If a ray bisects an angle of a triangle, then it divides the opposite side of the angle into segments proportional to the other two sides.