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Understanding Similar Figures

Answer Keys Here

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

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.

  • Quiz 1 - Which angle corresponds to
  • Quiz 2 - What is the ratio of side AB length to the length of its corresponding side?
  • Quiz 3 - Which angle corresponds to