Postulates/Theorems
By: Jack Eike
1. Angle-Angle Similarity Theorem (AA~)
This theorem is used for proving triangles similar. When you have two pairs of angles that are congruent, then those two triangles are congruent.
2. Side-Side-Side Similarity (SSS~)
This theorem is used for proving triangles similar. When you have three pairs of sides that are proportional, then those two triangles are congruent.
3. Side-Angle-Side Similarity (SAS~)
This theorem is used for proving triangles similar. When you have two pairs of sides that are proportional and one pair of angles that are congruent, then those two triangles are congruent.
4. Triangle Proportionality Theorem
If there is a line that is parallel to the base of a triangle, then the two sides that it intersects are proportional.
5. Triangle Angle Bisector Theorem
When an ray bisects an angle in a triangle and intersects the opposite side, the two segments that are made are proportional.
6. Two-Transversal Proportionality Theorem
When three parallel lines are intersected by two transversals, then the segments that are created on the transversals are proportional.
I choose these theorems because they are the base theorems that you use to either prove triangles similar or prove that the the segments are proportional. They are also the main theorems we really focused on in this unit because they are so important to understanding this concept of similar triangles and also triangle proportions.