The Congruent Twins' Transformation Talents

Contributor: Marlene Vogel. Lesson ID: 10623

What if a triangle looked in a mirror? What if it slid across the room? Learn how congruent shapes can transform. You'll complete hands-on practice AND create your own dance!


Geometry, Plane Geometry (2D)

learning style
Auditory, Kinesthetic, Visual
personality style
Golden Retriever
Grade Level
Middle School (6-8)
Lesson Type
Dig Deeper

Lesson Plan - Get It!


The Shapes Family

Once upon a time, there was a family who had a father (square), a mother (triangle), and three pairs of congruent twins. The twins were squares, triangles, and circles. Their family portrait is below:

 shapes family

This family is very unique!

Not only does this family have 3 pairs of congruent twins, but each set of twins has a special talent. Mr. and Mrs. Shape, in hopes of keeping their children physically fit, bought a coordinate plane for the children to play on outside.

The children took turns playing on the coordinate plane, one set of twins at a time. After a while, Mr. and Mrs. Shape began to notice that each set of twins could perform geometric transformations!

The squares did translations; the triangles did reflections, and the circles did rotations!

  • What exactly were the twins doing, and how did they do it?

Read on to find out!

Let's start with the vocabulary!

Congruent shapes are identical to each other, which means they have the same shape and the same size.

congruent example:


not congruent example:

not congruent

The neat thing about shapes is that they can go through what are called transformations. Transformations are changes in the positions of the shapes such as:

  • flipping over (reflection)
  • turning around a center point (rotation)
  • sliding to a different location (translation)

It all starts with the coordinate plane. The coordinate plane contains two axis (x and y) that intersect at a point (0,0).

coordinate plane:

coordinate plane

When we put a shape onto the coordinate plane, we can start making those transformations!

We can flip it over. This is called reflection:


We can turn it around a center point. This is called rotation:


Or, we can just slide it to a different position. This is called a translation:


Look over these terms and examples until you remember what each one means. Then, take this short quiz to check your understanding:

Now, move over to the Got It? page, where you'll practice making your own transformations!

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