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:

**Rotation**(Turn): Turns a figure around a fixed point.**Reflection**(Flip): Flip of figure over a line where a mirror image is created.**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:

**Rotation**(Turn): Turns a figure around a fixed point.**Reflection**(Flip): Flip of figure over a line where a mirror image is created.**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.

- Congruent Worksheet (1 of 3)
- Congruent Worksheet (2 of 3)
- Congruent Worksheet (3 of 3) – Congruence in Everyday Life!