This video lesson is designed for 6-12-year-old children. It helps them understand the geometric concept of similarity, congruency, and equivalency and how they differ using insets. It also guides the child to create their own insets at home.

Let us understand each concept one by one.

What is Congruency?

Any two or more objects that are identical in every respect: same size, same shape, and occupy same space are congruent. The symbol for congruency is ≌.
The video shows the child a pair of triangles and tells them how they are congruent.

What is Similarity?

Any two or more objects that are identical in shape are similar. The symbol for similarity is ∾.
The video shows how the two rectangles have the same shape but don’t have the same size and don’t occupy the same space. Thus, they are similar rectangles.

What is Equivalency?

Any two objects of the same size, occupy the same space, and have different shapes are equivalent. The symbol for equivalence is ≣.
The video shows how two triangles together form a square (same size) and occupy the same space are equivalent.

Congruency, similarity, and equivalency are fundamental concepts that deal with relationships. These concepts help the child to build social connections and research for reasons behind the facts. It also helps them in understanding the workfow of economy, finance, and various business operations.

In this video, the triangles, rectangles, and squares used to understand the concept are called Insets of Equivalence Cabinets.

What are the Insets of Equivalence Cabinet?

The Equivalent Figure Material is also known as Insets of Equivalence Cabinet. It helps understand the relationship of equivalent figures, leading to the discovery of area and theorems. This material consists of 13 green metal trays; each tray has a set of red metal insets.

The Insets of Equivalence Cabinet is one of the fascinating collections of materials in the Montessori Elementary environment. Each drawer contains a different collection of insets. The look of equivalency cabinets is the same as Metal Inset and Fraction Inset materials.

Firstly, Geometric concepts such as congruency, similarity, and equivalence of shapes are introduced with these various illustrations. Then the children learn the formula for calculating the area of shapes such as the rhombus and triangle. The final insets teach the children about the Pythagorean Theorem and the mathematical formulas of Euclid, the Greek mathematician who is historically considered the “father of geometry.”

This video also guides children to create an Equivalence Cabinet at home. Let us understand how?

  1. Take a cardboard and cut it into two equal triangles, two different sized rectangles, and two squares.
  2. Cut one of the squares diagonally to get two triangles.
  3. Paste a thumb pin to the cut-outs for easy hold.


Watch the video to understand the difference between congruency, similarity, and equivalency with the help of insets.

For more mathematical lessons, click here.


Video created by Sharmeen Niazi (Archgate Montessori Academy, Plano, TX)

Elementary | Math | Geometry | Equivalency (English)

This video has been added and used with the author’s permission. It is also available on the author’s YouTube, here.


  • Elementary
  • English
  • Math