Lesson Plan

Congruency, Similarity, and Scale Factor


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Big Ideas




In this lesson, students will learn methods for identifying congruent and similar figures. They will use the relationship between corresponding parts to make decisions regarding pairs and sets of figures. Students will use the concept of scale factor to consider the changes in figures as they are reduced and enlarged. Students will:

  • identify congruent and similar polygons.
  • explain the characteristics that determine similarity and congruence.
  • discover the relationship between scale factor, perimeter, and area.
  • graph figures and their images (including congruent, similar, and non-similar).
  • write and use rules for reducing and enlarging figures, such as (x, y) → (2x, 2y).
  • consider congruence and similarity of circles.
  • apply congruence and similarity concepts to solve problems with missing values.
  • apply the concept of scale factor to scale drawings and maps.

Essential Questions

  • How can we use the relationship between area and volume to help us draw, construct, model, and represent real situations and/or solve problems of area and volume?


  • Congruent: Having the same shape and size.
  • Corresponding: Parts of a figure, such as sides and angles, which are in the same relative position in two different figures.
  • Similar: Having the same shape, but a different size which is proportional to another figure.
  • Scale Factor: The ratio of the lengths of the corresponding sides in similar figures, the number multiplied by the side length measures of one figure to create a reduced or enlarged image. [IS.1 - Preparation]


180–210 minutes [IS.2 - All Students]

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Related Materials & Resources

The possible inclusion of commercial websites below is not an implied endorsement of their products, which are not free, and are not required for this lesson plan.

  • Game in which student names the coordinate to locate aliens


  • Game in which student selects a coordinate pair from a list of 4 choices to catch a mole, multiple difficulty levels


  • Compares side length and area as scale factor changes


  • Video clip reviewing definition of similarity and corresponding parts


  • Calculate the surface area and volumes of a variety of rectangular and triangular prisms by adjusting the dimensions, may use for enrichment


  • Interactive question session on similar and congruent figures


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