Unit 6: Similarity
In this unit, we will review how ratios and proportions connect with the concept of similarity. We frequently consider objects to be similar to one another due to their design, size, or some other quality. In geometry, however, strict rules apply for determining whether two shapes are similar.
Completing this unit should take you approximately 5 hours.
6.1: Similar Polygons
In this section, we explore the precise meaning of similarity when describing polygons. We will look at triangles and then larger polygons.
6.2: Similarity Postulates
When describing similarity, we can use a series of postulates to determine if two polygons are similar.
6.3: Angle-Angle Similarity and Indirect Measurement
There are different ways to determine similarity between triangles. One method is called angle-angle (AA) similarity which tells us that if two triangles have two congruent angles, the two triangles must be similar. If triangles have AA similarity, we can use indirect measurement to determine unknown measurements within one of the triangles.
6.4: Side-Side-Side and Side-Angle-Side Similarity
Other types of similarity are side-side-side (SSS) and side-angle-side (SAS). In SSS similarity, we see that if the sides of two triangles are proportional, the triangles are similar. In SAS similarity, we see that if two sides and one angle are proportional between two triangles, the two triangles are similar.
6.5: Triangle Proportionality, Parallel Lines and Transversals
After learning the similarity criteria for triangles, we can apply our knowledge to solve more complex problems involving triangles.