Geometry Unit 9 (Lessons 3-4)

Converse of the Triangle Proportionality Theorem

If a line divides two sides of a triangle proportionally, then the line is parallel to the third side of the triangle.

Triangle Proportionality Theorem

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

Corollary 2 of the Triangle Proportionality Theorem:

If one transversal intersects three or more parallel lines so that it is divided into congruent segments, then any transversal that intersects the same parallel lines will be divided into congruent segments.

Side-Side-Side (SSS) Similarity Theorem:

If the measures of the three sides of one triangle are proportional the measures of the corresponding three sides of another triangle, then the triangles are similar.

Corollary 1 of the Triangle Proportionality Theorem:

If three or more parallel lines intersect two transversals, then they divide the transversals proportionally.

Angle-Angle (AA) Similarity Postulate:

If two angles of one triangle are congruent to two angles of another triangle, then the two triangles are similar.

Side-Angle-Side (SAS) Similarity Theorem:

If two sides of one triangle are proportional to two sides of another triangle and their included angles are congruent, then the triangles are similar.