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Chapter overview
Learning goals
Learning Goals
Maths
Summary
Construction involves working with angles and lines to scale without a protractor. Constructions are performed using a straight edge and a compass. There are four main constructions that you need to be able to perform.
A straight edge is a ruler without any markings that indicate length.
A compass is an instrument that consists of a pointed tip and a hole to place a pencil. It is used to draw circles by rotating the compass about the tip.
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Two lines are perpendicular if they meet at right angles (or $90\degree$).
A line is bisected if it is split exactly in half.
The perpendicular bisector of a line is another line that splits the line in half while meeting it at right angles.
The grey line above is a perpendicular bisector of the line $RS$.
1. | Set the compass to a length that is greater than half the length of the line. |
2. | Using this set length, draw arcs about both ends of the line. |
3. | Using a straight edge, draw a line between the two points where the arcs intersect. This line is the perpendicular bisector. |
Or, presented visually:
STEP 1 | STEP 2 |
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Note: When performing constructions, always leave the construction lines visible. Do not rub them out!
The angle bisector of an angle is a line that splits an angle exactly in half.
1. | Set the compass to a set length. Draw an arc about the point where the angle is so that the arc touches the two lines that the angle is between. |
2. | At each of these points where the arc meets the lines, draw an arc with the same set length. This will result in two more arcs: one from each point. |
3. | Draw a straight line from the vertex to the point where both arcs meet. This line is the angle bisector. |
Or, presented visually:
This construction involves drawing a line through a given point that is perpendicular to another line.
1. | Set the compass to a set length. Draw an arc around the point so that it intersects the line at two distinct points. |
2. | At each of those points, draw an arc. This will result in two more arcs: one from each point. Make sure the length is set such that the two arcs intersect. |
3. | Draw a straight line from the given point to the point where both arcs meet. This is the perpendicular line. |
Or, presented visually:
STEP 1 | STEP 2 | STEP 3 |
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This construction is very similar to the above construction, but this time, the point is on the line.
1. | Set the compass to a set length. Draw an arc around the given point so that it intersects the line in two points. |
2. | At each of these points, set the compass to a slightly longer length and draw an arc. This will result in two more arcs: one from each point. Make sure the length is such that the two arcs intersect. |
3. | Draw a straight line from the given point to the point where both arcs meet. This is the perpendicular line. |
Or, presented visually:
STEP 1 | STEP 2 | STEP 3 |
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Construction involves working with angles and lines to scale without a protractor. Constructions are performed using a straight edge and a compass. There are four main constructions that you need to be able to perform.
A straight edge is a ruler without any markings that indicate length.
A compass is an instrument that consists of a pointed tip and a hole to place a pencil. It is used to draw circles by rotating the compass about the tip.
| |
Two lines are perpendicular if they meet at right angles (or $90\degree$).
A line is bisected if it is split exactly in half.
The perpendicular bisector of a line is another line that splits the line in half while meeting it at right angles.
The grey line above is a perpendicular bisector of the line $RS$.
1. | Set the compass to a length that is greater than half the length of the line. |
2. | Using this set length, draw arcs about both ends of the line. |
3. | Using a straight edge, draw a line between the two points where the arcs intersect. This line is the perpendicular bisector. |
Or, presented visually:
STEP 1 | STEP 2 |
| |
Note: When performing constructions, always leave the construction lines visible. Do not rub them out!
The angle bisector of an angle is a line that splits an angle exactly in half.
1. | Set the compass to a set length. Draw an arc about the point where the angle is so that the arc touches the two lines that the angle is between. |
2. | At each of these points where the arc meets the lines, draw an arc with the same set length. This will result in two more arcs: one from each point. |
3. | Draw a straight line from the vertex to the point where both arcs meet. This line is the angle bisector. |
Or, presented visually:
This construction involves drawing a line through a given point that is perpendicular to another line.
1. | Set the compass to a set length. Draw an arc around the point so that it intersects the line at two distinct points. |
2. | At each of those points, draw an arc. This will result in two more arcs: one from each point. Make sure the length is set such that the two arcs intersect. |
3. | Draw a straight line from the given point to the point where both arcs meet. This is the perpendicular line. |
Or, presented visually:
STEP 1 | STEP 2 | STEP 3 |
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