Summary of Chapter
This chapter will explain what makes triangles congruent, as well as ways to determine that two triangles are congruent. It will also explain what makes triangles similar. To see the textbook related to this chapter, see the Wikibook chapter.
Triangle Congruency
Definition: Two or more triangles are congruent if all three of their corresponding angles and all three of their corresponding line segments are congruent.
Triangle Congruency Postulates
1) The SSS Triangle Congruency Postulate
- Postulate: Every SSS (Side-Side-Side) correspondence is a congruence.
2) The SAS Triangle Congruency Postulate
- Postulate: Every SAS (Side-Angle-Side) correspondence is a congruence.
- Note: It is important that the angle is included; that is, it is adjacent to the two congruent sides.
3) The ASA Triangle Congruency Postulate
- Postulate: Every ASA (Angle-Side-Angle) correspondence is a congruence.
- Note: It is important that the side is included; that is, it is adjacent to the two congruent angles.
Congruency vs. Similarity
Congruency is, simply put, when two things have the same size and the same shape. Similarity, however, has only part of that definition: two things are similar if they have the same shape, but not necessarily the same size. Any two circles, for example, are similar, because they have the same shape, but one circle can be huge and another small. The same goes for all squares and equilateral triangles.
Triangle Similarity
Definition: Two or more triangles are similar if their angles are congruent and their sides are proportional.
Triangle Similarity Theorems
1) The AA Triangle Similarity Theorem
- Theorem: Every AA (Angle-Angle) correspondence is a similarity.
2) The SSS Triangle Similarity Theorem
- Theorem: Every SSS (Side-Side-Side) proportional correspondence is a similarity.