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The student should be able to construct using geometry equipment and master the various mathematical notations on lines. The 3 essential properties must be known in order to be able to carry out demonstrations in class of sixth.
I. Point, segment, line and half line
1. vocabulary, representations and notations
2. Alignment and belonging
Aligned points are points that belong to the same line.
Example:
In the figure below, points A, B and M are aligned.
- The point M belongs to the line (AB). We note
. - The point N does not belong to the line (AB). .
3. Distance between two points
The distance between two points is the length of the shortest path between these two points. This is the length of the segment that joins these two points.
Example:
The distance between points A and B is 2.5 cm.
We note: AB = 2.5 cm.
4. Middle of a segment
The middle of a segment is the point on the segment that divides it into two segments of equal length.
Example:
The point M is the middle of the segment [AB].
Indeed: the points A, M and B are aligned and MA=MB.
II. Perpendicular lines
1. secant lines
Two intersecting lines are two lines that have only one point in common.
Example:
The lines (d) and (d’) are secant at A.
2. Perpendicular lines
Two perpendicular lines are two intersecting lines that form four right angles.
Example and notation:
The ruler and the square are used to draw two perpendicular lines.
The lines (d) and (d’) below are perpendicular at A.
We note .
3. Distance from a point to a line
The distance from a point to a line is the length of the shortest path between that point and the line.
The distance from a point A to a line (d) is the distance (AH) between A and H, the foot of the perpendicular led from A to the line (d).
4. The perpendicular bisector of a segment
The perpendicular bisector of a segment is the line that is perpendicular to the segment at its center.
Example:
The line (d) is the perpendicular bisector of the segment [AB].
Indeed:
- The line (d) is perpendicularto the line (AB);
- The line (d) cuts the segment [AB] in its middle.
III. Parallel lines
1. parallel lines
Two parallel lines are two lines that do not intersect.
Example and notation:
The lines (d) and (d’) are parallel.
We note (d)//(d’).
Remark:
When points A, B and C are aligned, the lines (AB) and (AC) are said tocoincide.
2.distance between two parallel lines
The distance between two parallel lines is the length of the shortest path between these two lines.
The distance between two parallel lines (d) and (d’) is the length of a segment [AB]perpendicular to these two lines with A a point of (d) and B a point of (d’).
3. two properties
If two lines are perpendicular to a third, then they are parallel.
If two lines are parallel, and a third line is perpendicular to one, then it is also perpendicular to the other.
Did you learn about parallel and perpendicular lines in 6th grade?
Un QCM de maths sur les droites parallèles et perpendiculaires en 6ème.
Skills to learn about parallel and perpendicular lines:
- Know how to draw two parallel or perpendicular lines using a ruler and a square;
- Know the mathematical notation for a line;
- Know the membership symbol and the parallelism symbol;
- Know the three properties in order to demonstrate.
This course is in accordance with the official programs of thenational education.
In addition, you can continue with the exercises on straight lines in the sixth grade.
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