Angle-Angle Similarity Theorem
If two angles of one triangle are congruent to two angles of another triangle, then the triangles are similar.
Side-Side-Side Similarity Theorem
If the corresponding sides of two triangles are proportional, then the triangles are similar.
Side-Angle-Side Similarity Theorem
If two of the corresponding sides of two triangles are proportional and the included angles are congruent, then the triangles are similar.
Angle bisector/Proportional Side Theorem
A bisector of an angle in a triangle divides the opposite side into two segments whose lengths are in the same ratio as the lengths of the side adjacent to the angle.
Triangle Proportionality Theorem
If a line parallel to one side of a triangle intersects the other two sides, then it divides the two side proportionally.
Converse of the Triangle Proportionality Theorem
If a line divides two sides of a triangle proportionally, then it is parallel to the third side.
Proportional Segments Theorem
If three parallel lines intersect two transversals, then they divide the transversals proportionally
Triangle Midsegment Theorem
The midsegmentof a triangle is a parallel to the third side of the triangle and half the measure of the third side of the triangle.
Right Triangle/Altitude Similarity Theorem
If an altitude is drawn to the hypotenuse of a right triangle, then the two triangles formed are similar to the original triangle and to each other.
Right Triangle Altitude/Hypotenuse Theorem
The measure of the altitude drawn from the vertex of the right angle of a right triangle to its hypotenuse is the geometric mean between the measures of the two segments of the hypotenuse.
Right Triangle Altitude/Leg Theorem
If the altitude is drawn to the hypotenuse of a right triangle, each leg of the right triangle is the geometric mean of the hypotenuse and the segment of the hypotenuse adjacent to the leg.
