 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

Definition:

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

Example:

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

It is also said that:

• is the symmetry of with respect to the line (d).
• is the symmetric of . Ownership:

Axial symmetry with respect to a line preserves :

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

Example:

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’.

• and .
• Triangles ABC and A’B’C’ have the same area. ### 2. axis of symmetry of a figure

Definition:

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

Example:

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

Symmetry about a line is also called axial symmetry.

### 3. symmetry of a point

Definition:

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’]. M belongs to (d).

The symmetric of the point M with respect to the line (d) is the point M itself. ## II.symmetry of a line and a segment

### 1.symmetric of a line

Ownership:

The symmetric of a line about a line is a line. ### 2.symmetrical of a segment

Ownership:

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

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

Example:

• 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: • 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.

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