Goal: The purpose of this lesson is to enable students to see the relationship between triangle similarity and
proportions. While the angle-angle relationship does not necessarily lead to congruence, its properties are still
imperative to similarity.
How Does it Work?Indirect measurement utilizes the Law of Reflection, stating that the angle at which a ray of light
(ray of incidence) approaches a mirror will be the same angle in which the light bounces off (ray of reflection). This
method is the basis of reflecting points in real world applications such as billiards and miniature golf.
Additional Example:Pere Noel is shopping for a Christmas tree. The tree can be no more than 4 meters tall. Mary
finds a tree that casts a shadow of 2 m, whereas Mary (120 cm tall) casts a shadow of 0.8 m. Will the tree fit in Pere
Noel’s room?Yes, the tree is3 meterstall, therefore, it will fit in the room.
Similarity by SSS and SAS
Pacing:This lesson should take one class period
Goal:The purpose of this lesson is to extend the SSS and SAS Congruence Theorems to include similarity.
Visualization!Now may be a good time to discuss similarity and congruency by drawing a Venn diagram. Students
may ask the question, “How can triangles be congruent and similar simultaneously?” The diagram below will help
clear questions.
Similar figures are usually thought to be produced under dilations (size changes). However, congruent figures are
a specific type of similarity transformation. Therefore, rotations, reflections, glide reflections, translations, and the
identify transformation all yield similar figures.
Similarity Transformations
Pacing:This lesson should take one class period
Goal: Dilations produce similar figures. This lesson introduces the algorithm to produce similar figures using
measurements and a scale factor,k
Chapter 1. Geometry TE - Teaching Tips