Indeed, we shall prove that every similarity is one of the following four distinct types: an isometry, a stretch, a stretch reflection or a stretch rotation. We begin with another look at the family of …

Similarity is a very useful tool that we will get into a little earlier than Euclid does in the Ele-ments by developing some of the basic properties of similar triangles from high-school trigonometry.

Let 4ABC and 4DEF satisfy SAS with AB ˘=DE, AC ˘=DF, and \BAC ˘=\EDF. To show congruence, superimpose the triangles so that A is on D and AB is on DE. Then B is on E since AB ˘=DE. In …

How to help: Remind students that we determine similarity based on specific criteria, not just by eyeballing it. Just because they look similar doesn’t mean they are.

The activities at the beginning of Stretching and Shrinking build on students’ notions about similarity as they explore figures with the same shape. They draw similar figures using rubber bands and …

Practice Quiz Similarity 1. Identify the pairs of congruent angles and corresponding sides. An Corresponding Sides whether ∆JLM ∆NPS. If so, th

State if the triangles in each pair are similar. If so, state how you know they are similar and complete the similarity statement. Find the missing length. The triangles in each pair are similar. Free trial …

Example: Write a similarity statement relating the three triangles in each diagram. Example: Find the geometric mean of each pair of numbers We can use the geometric mean to write proportions using …

10 In the diagram below, ABC ∼ DEF. If AB = 6 and AC = 8, which statement will justify similarity by SAS? 11 In the diagram below, AC = 7.2 and CE = 2.4. ABC ∼ EDC? 12 Using the information given …

Definition of Similarity • Two figures F and G are similar if G = T(F), where the transformation T is a similarity. Dilations