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Congruent Triangles

Working through the lesson below will help your child to understand that congruent figures can be determined by a figure rotation, reflection, or translation or any combination of the three. It will also help them to identify the types of transformations in a sequence.

Learning Takeaways: After this lesson, students will be able to:

  • Identify the characteristics of congruent figures
  • Perform transformations on a figure (rotation, reflection, and translation)
  • Identify the types of transformations in a sequence

Make sure your child is familiar with the vocabulary below:

  • Two-dimensional figure: A figure that lies in a plane.

Congruent Triangles (and other figures)

This section will help your child to identify the characteristics of congruent figures.

Two figures are congruent if they are the:

  • Exact same shape
  • Exact same size
    • Angle measures are equal
    • Line segments are equal

Look at the example below.

Discuss the examples and questions below with your child regarding whether the figures are congruent.

Which figure is congruent to figure C shown below?

Figure b. is congruent.

Transformations : Rotations, Reflections, & Translations

This section will help your child to perform a transformation (rotation, reflection, and translation) on a figure .

Make sure your child is familiar with the vocabulary below:

  • Transformation moves a figure from its original place to a new place.
  • Angle of Rotation: How big the angle is that you rotate a figure.  Common angle rotations are 45°, 90°, 180°.
  • Isometric Transformation: A transformation that does not change the size of a figure.

There are three types of transformations. Alternative names are in parenthesis:

  1. Rotation (Turn): Turns a figure around a fixed point. 
  2. Reflection (Flip): Flip of figure over a line where a mirror image is created.
  3. Translation (Slide or glide): Sliding a shape to a new place without changing the figure.

Rotations, reflections, and translations are isometric.  That means that these transformations do not change the size of the figure.  If the size and shape of the figure is not changed, then the figures are congruent.

Explore and discuss the examples of transformations below with your child.

Try It! Find a flat object in your home that can easily be moved (small book, calculator, drink coaster, coin, etc.)  Perform each transformation using that object.

Multiple Transformations

This section will help your child to understand that congruent figures can have more than one transformation.

Make sure your child is familiar with the vocabulary below:

  • Sequence: A group of things arranged in a certain order.  Commonly known as a pattern.

Recapping from earlier in his lesson, there are three types of transformation:

  1. Rotation (Turn): Turns a figure around a fixed point. 
  2. Reflection (Flip): Flip of figure over a line where a mirror image is created.
  3. Translation (Slide or glide): Sliding a shape to a new place without changing the figure.

Two Transformations

Try It! Look at the figure below. What transformations does parallelogram Z perform?

Congruent Figures Worksheets

Click the links below and get your child to try the worksheets on congruent figures and practice with questions based on what is shown above.