Constructions
Level 7
The objectives of this unit are to use compasses to construct
* a triangle with given side lengths;
* the bisector of an angle;
* the perpendicular bisector of a line;
* the perpendicular from a point to a line;
* the perpendicular to a line from a point on that line.
Constructing a triangle
Example:
Construct a triangle with sides 12cm, 7cm and 8cm.
Bisecting an angle
To bisect means to cut exactly in half.
Example: Bisect the angle shown below:
Solution:
Notes on bisecting an angle: Every point on the line that bisects the angle is the same distance from both arms of the angle, i.e. every point on the line AD is equidistant from the lines AB and AC.
Constructing the perpendicular bisector of a line
Example: Construct the perpendicular bisector of the line AB shown below.
Note: The perpendicular bisector of AB is a line that is at right angles to AB and which cuts AB in half.
Solution:
Notes on constructing the perpendicular bisector of a line: Every point on the line CD is the same distance (i.e. equidistant) from the points A and B.
Constructing the perpendicular from a point to a line
Example: On the diagram below, construct the perpendicular from the point P to the line AB:
Solution:
Constructing the perpendicular to a line from a point P on the line
Example: Construct the perpendicular to the line AB from point P:
Solution:
General points on constructions:
1) Hold your compasses using the handle at the top.
2) Don’t put too much pressure on your compasses, otherwise your compasses could widen.
3) Never rub out your construction lines!!