Constructions

For A.S 1.4 Use Geometric Techniques

to produce a pattern or object.Internal, 2 Credits

Hexagon Perp. Bisector Angle Bisector Perp. Pt on line Perp. Pt off line Parallel Line

Mathematical Drawings using a Compass and

Straight Edge.

Constructing a hexagon:eg. construct a hexagon with 6cm sides (click once to start)

1. Set your compass to the required side length (6cm in this case)

6 cm

2. Construct a circle using this radius.

3. Starting anywhere on the circumference, “walk” your compass

4. Join up all your arc crossings.

around the circumference, scribing arcs as you go.

Hexagon Perp. Bisector Angle Bisector Perp. Pt on line Perp. Pt off line Parallel Line

You now have a regular hexagon with 6 cm sides.

6 cm

Perpendicular Bisector or MediatorTo Bisect Line AB: (click once to start)

A

B

1. With Compass point on A, scribe the blue arcs.

2. With Compass on B scribe the green arcs.

3. Join the arc crossings to show the mediator.

NB: Point C is called the “Midpoint” of line AB

C

Hexagon Perp. Bisector Angle Bisector Perp. Pt on line Perp. Pt off line Parallel Line

Angle Bisector (click once to start)

•Make two arcs (same radius) from B which cut AB at D and BC at E.•Make two arcs (same radius) from D and E – which meet at arc crossing, F.•Join FB.

B

A

CD

E

F

Hexagon Perp. Bisector Angle Bisector Perp. Pt on line Perp. Pt off line Parallel Line

Perpendicular through a Point on the line: (click once to start)

•Make two arcs (same radius) from C which cut AB at D and E. (Extend AB if necessary).

C

B

A

F

D

E

•Setting compass to a larger radius, make arcs from D and E, crossing at F.•Join FC.

Hexagon Perp. Bisector Angle Bisector Perp. Pt on line Perp. Pt off line Parallel Line

Perpendicular through a Point **NOT** on the line: (click once to start)

•Make two arcs (same radius) from C which cut AB at D and E. (Extend AB if necessary).

B

A

F

D

E

•Setting compass to a larger radius, make arcs from D and E, crossing at F.•Join FC.

CHexagon Perp. Bisector Angle Bisector Perp. Pt on line Perp. Pt off line Parallel Line

A line parallel to, and a certain distance from a line: (click once to start)

Eg. construct the line 2cm above line AB.

B

A

•Set the compass to the distance required – 2cm in this case.

•Make a number of arcs (same radius) from line AB. (ie with the point of the compass at random points on the line)

•Rule a line over the top of the “waves”.

2 cm

Hexagon Perp. Bisector Angle Bisector Perp. Pt on line Perp. Pt off line Parallel Line

end

Hexagon Perp. Bisector Angle Bisector Perp. Pt on line Perp. Pt off line Parallel Line