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.

These triangles are congruent. They are the exact same size AND shape. If you slid triangle A to the right, it would exactly cover triangle B. This is called a translation. You will learn more about translations in the next section of this lesson. |

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

These rectangles are not congruent. They are not the same size. | |

These triangles are not congruent. They are the same size but not the same shape. Triangle B is a right triangle. Triangle A is an isosceles triangle. | |

Are these two parallelograms congruent? Are they the exact same shape and the exact same size? Answer: They are the same shape and size so they are congruent. See more about rotations later in this lesson. |

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.

Examples of Transformations | |

Rotation | Triangle A is a 90° rotation of triangle B. The angle of rotation of is 90 degrees. Notice how the angle created between the 2 figures is equal to the angle of rotation. |

Reflection | Reflections “flip” a figure over a line (often referred to as a line of symmetry).Reflections are mirror images and appear “backwards” from the original figure. |

Translation | A translation slides or glides a figure from one place to another. A translation cannot have any rotation (or else it would be a rotation). |

**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 **

Triangle B has performed two transformations. It is rotated 90° and translated. Triangle B is a rotation of triangle A because it turned 90°. It was also slid up and to the right, making a translation. | |

What two transformations could have been performed here? Hint: Figure 2 is a mirror image of figure 1. Figure 2 is a reflection and translation of figure 1. The figure is a reflection because it flipped. It is a translation because it is moved to another place, without rotating it. This is also called a glide reflection. |

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

Think: Does figure Z face the same direction? Are corresponding parts of the parallelogram parallel each other? Are the figures in the same quadrant of the Cartesian plane? |

**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!