Axial symmetry: 6th grade math course download pdf.

A course on axial symmetry with the definition and properties as well as the method of constructing the symmetric of a point with a square and a compass. We will end this lesson with the symmetry of a point, a line and the axes of symmetry of a figure.
The student should be able to construct the image of a figure by axial symmetry of axis (d) using the geometry material. He/she should also know all the conservation properties of central symmetry concerning the lengths of segments, alignment, the measure of an angle or the perimeter or area of a figure. The assimilation of the different properties of central symmetry is essential in order to be able to carry out demonstrations in geometry in the sixth grade.

I. Axial symmetry

1. symmetrical figures


Two figures are symmetrical about a line (d) when they overlap by folding about the line (d).


the figures F and F' below are symmetrical with respect to the line (d).

It is also said that:

  • F' is the symmetry of F with respect to the line (d).
  • F is the symmetric of F'.

axial symmetry of a flower


Axial symmetry with respect to a line preserves :

  • the lengths;
  • alignment;
  • angle measurements;
  • areas.


The rectangular triangles ABC and AB’C’ below are symmetrical about the line (d).

  • AB=A’B’, AC=A’C’, BC=B’C’.
  • Point M is aligned with points A and C.

Its symmetric M’ is also aligned with points A and C’.

  • \widehat{ABC}=90^{\circ} and \widehat{AB'C'}=90^{\circ}.
  • Triangles ABC and A’B’C’ have the same area.

conservation symmetry

2. axis of symmetry of a figure


A line is an axis of symmetry of a figure when that figure coincides with its symmetry about that line.


The red line is the axis of symmetry of this figure.

axis of symmetry


Symmetry about a line is also called axial symmetry.

3. symmetry of a point


M does not belong to (d).

The symmetric of the point M with respect to the line (d) is the point M’ such that the line (d) is the bisector of the segment [MM’].

Symmetric of a point

M belongs to (d).

The symmetric of the point M with respect to the line (d) is the point M itself.

Invariant point

II.symmetry of a line and a segment

1.symmetric of a line


The symmetric of a line about a line is a line.

Symmetric of a line

2.symmetrical of a segment


The symmetry of a segment with respect to a line (d) is a segment with the same length.

Axial symmetry


The symmetric of a polygon about a line is a polygon that has the same number of sides.


  • The symmetric about a line of a triangle is a triangle.
  • The symmetric about a line of a square is a square.

Did you get that lesson on axial symmetry in 6th grade?

La symétrie axiale

QCM sur la symétrie axiale en 6ème.

Things to remember:

Skills to be assimilated on the circle:

what to remember

  • Know the definition of symmetrical;
  • Know how to draw the symmetrical line using geometry equipment (ruler, compass, square and protractor);
  • Know the properties of the conservation radius of axial symmetry in order to write demonstrations.

This course is in accordance with the official programs of thenational education.

In addition, you can consult the exercises on axial symmetry in the sixth grade.

Cette publication est également disponible en : Français (French) العربية (Arabic)

Télécharger puis imprimer cette fiche en PDF

Télécharger ou imprimer cette fiche «axial symmetry: 6th grade math course download pdf.» au format PDF afin de pouvoir travailler en totale autonomie.

D'autres fiches dans la section 6th grade math class

Télécharger nos applications gratuites Mathématiques Web avec tous les cours,exercices corrigés.

Application Mathématiques Web sur Google Play Store.    Application Mathématiques Web sur Apple Store.    Suivez-nous sur YouTube.

D'autres articles analogues à axial symmetry: 6th grade math course download pdf.

  • 93
    Integers: 6th grade math course in PDF.A math course in sixth grade (6ème) In this free lesson on integers, which you can download in PDF format, we will deal with the decomposition and the position of a digit as well as the location on a graduated line in order to be able to compare, afterwards, two…
  • 93
    Proportionality and percentages: 6th grade math course in PDF.Math course on proportionality and percentages This lesson covers the definition of proportionality and its additivity as well as the passage through the unit and percentages as well as the coefficient and the proportionality table. The student should be able to show if a table is proportional or not and…
  • 93
    Angles: 6th grade math lessons for download PDF.A sixth grade math lesson on angles to develop students' knowledge and skills in geometry. An angle is a measure of the opening between two straight lines that meet at a common point called the vertex of the angle. It is usually expressed in degrees or radians. In this chapter,…
Les dernières fiches mises à jour

Voici la liste des derniers cours et exercices ajoutés au site ou mis à jour et similaire à axial symmetry: 6th grade math course download pdf. .

  1. الوظائف والحدود: تمارين الرياضيات في السنة النهائية مصححة بتنسيق PDF.
  2. Functions and limits: senior math exercises corrected in PDF.
  3. Fonctions et limites : exercices de maths en terminale corrigés en PDF.
  4. الوظائف المعتادة: دورة الرياضيات في المركز الثاني للتحميل بصيغة PDF.
  5. Usual functions : maths course in 2nd grade to download in PDF.

Inscription gratuite à Mathématiques Web. Mathématiques Web c'est 2 145 971 fiches de cours et d'exercices téléchargées.

Copyright © 2008 - 2023 Mathématiques Web Tous droits réservés | Mentions légales | Signaler une Erreur | Contact

Scroll to Top
Mathématiques Web