Lesson 6Similarity
Learning Goal
Let’s explore similar figures.
Learning Targets
I can apply a sequence of transformations to one figure to get a similar figure.
I can use a sequence of transformations to explain why two figures are similar.
Lesson Terms
- similar
Warm Up: Equivalent Expressions
Problem 1
Use what you know about operations and their properties to write three expressions equivalent to the expression shown.
Activity 1: Similarity Transformations (Part 1)
Problem 1
Triangle
Print Version
Triangle
![Triangle LME and larger, similar triangle EGH with a line running through their hypontenuse's](../../../../../../embeds/91b074d1--8.2.B1.Image.02.png)
Problem 2
Hexagon
Print Version
Hexagon
![Hexagon ABCDEF and larger hexagon GHIJKL](../../../../../../embeds/5ff0949a--8.2.B1.Image.03.png)
Are you ready for more?
Problem 1
The same sequence of transformations takes Triangle
![A circular grid with a small blue triangle, A near the center and green triangles B-E of varying sizes.](../../../../../../embeds/b0c3f143--8.2.B1.Image.04.png)
Activity 2: Similarity Transformations (Part 2)
Problem 1
Sketch figures similar to Figure A that use only the transformations listed to show similarity.
![Polygon labeled A.](../../../../../../embeds/960fa502--8.2.B1.Image.05.png)
A translation and a reflection. Label your sketch Figure B.
Pause here so your teacher can review your work.A reflection and a dilation with scale factor greater than 1. Label your sketch Figure C.
A rotation and a reflection. Label your sketch Figure D.
A dilation with scale factor less than 1 and a translation. Label your sketch Figure E.
Activity 3: Methods for Translations and Dilations
Problem 1
Your teacher will give you a set of five cards and your partner a different set of five cards. Using only the cards you were given, find at least one way to show that triangle
![A grid with point P in the upper left and then triangle ABC and larger triangle DEF. Side AB is 4 units and BC is 2 units. Side DE is 12 units and EF is 6 units.](../../../../../../embeds/907df285--8.2.B1.Image.08.png)
Lesson Summary
Let’s show that triangle
Two figures are similar if one figure can be transformed into the other by a sequence of translations, rotations, reflections, and dilations. There are many correct sequences of transformations, but we only need to describe one to show that two figures are similar.
![Blue triangle ABC and green triangle DEF.](../../../../../../embeds/e9c42c98--8.2.B1.Image.10.png)
One way to get from
step 1: reflect across line
step 2: rotate
counterclockwise around step 3: dilate with center
and scale factor 2
Another way would be to dilate triangle