Unit 2, Lesson 6
Similarity
Grade 8
Preparation
Lesson Narrative
The purpose of this lesson is to define that two figures are similar if there is a sequence of translations, rotations, reflections, and dilations that takes one figure to the other. It is important to note that there are many different sequences that could show two figures are similar.
Students begin the lesson by studying pairs of triangles where some pairs are scaled copies of each other and some pairs are not. Next, in order to show that scaled copies are similar, students find and describe a sequence of transformations that takes one figure to the other using precise mathematical language (MP6). Students also practice sketching similar figures created using given transformations. An optional activity provides additional practice finding a sequence of transformations that show two figures are similar.
In future lessons, students will learn other methods for showing similarity, but in this lesson the focus is on the definition of similarity in terms of transformations.
- Comprehend that the phrase “similar figures” (in written and spoken language) means there is a sequence of translations, rotations, reflections, and dilations that takes one figure to the other.
- Justify (orally) the similarity of two figures using a sequence of transformations that takes one figure to the other.
Let’s explore similar figures.
Required Preparation
Provide access to geometry toolkits. For the digital version of the activity, acquire devices that can run the applet.
Provide access to geometry toolkits.
Two figures are similar if one can fit exactly over the other after transformations.
This figure shows triangle is similar to triangle .
- Rotate triangle around point .
- Then dilate it with center point .
- The image will fit exactly over triangle .
A sequence of transformations. Triangle ABC is rotated around point B and and then dilated with center point O to fit exactly over Triangle DEF. Triangle ABC is similar to triangle DEF.