## Understanding Similar Figures

#### Aligned To Common Core Standard:

**Grade 8 Geometry** - 8.G.A.4

What are Similar Figures? Let's start with a fun activity. On a piece of paper, draw a square. Just underneath it, draw another square, with the same measurements. Now take a look. Don't these figures look alike? These are called Similar Figures! Whenever two figures have the same shape, they are known as similar figures. In more depth, two figures are similar if their angles and the ratios of the length of their corresponding sides are equal too. To understand better, look up identical twins! They are the perfect example of what similar figures are. The symbol for denoting indicating similarity is “~”

### Printable Worksheets And Lessons

- Explain Congruence Step-by-Step Lesson- We go over all the things you need to know about congruent
and similar figures.

- Guided Lesson -
This somewhat mimics the previous standard in a lot of ways (G.3).

- Guided Lesson Explanation
- A very basic explanation will do it for this one. It should be
easy to follow.

- Independent Practice
- How did one shape become another? Untwist the plot of these shapes
on the grids.

- Matching Worksheet
- I know it would have helped if I used the same shape over and
over, but this gives students some confidence.

- Exploring Similar Figures Five Pack - It is amazing what you can get out of two similar figures.

#### Homework Sheets

Each sheet builds upon the last sheet.

- Homework 1 - The figures have been dilated with a scale factor of ½ then reflected across the x-axis, making Figures B and B’ similar, but not congruent.
- Homework 2 - In this case, the scale factor of the dilation can be found by using the horizontal distances on the triangle. 90˚ clockwise rotation, translate 2 right and 4 up, dilation of 1/2.
- Homework 3 - Dilated with a scale factor of 4/2 then translate 3 right and 3 down, making Figures X and X’ similar. Since the shapes are not the same size, they are not congruent.

#### Practice Worksheets

Most students claim that these get progressively easier.

- Practice 1 - Describe the sequence of transformations that results in the transformation of Figure A to Figure B.
- Practice 2 - Figures are congruent if they are the same exact shape and size. Figures can be similar if they are the same shape, but different sizes.
- Practice 3 - Is Figure Z congruent to Figure Z’? How do you know? Explain.

#### Math Skill Quizzes

These are all about identifying corresponding angles.