Maths construction ppt

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Geometric Constructions

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Constructing
Midpoints & Perpendicular Bisectors

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Constructing the Midpoint & Perpendicular
bisector of a line segment
A B
C
D
Construction Lines
Construction Lines

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Constructing
Angle Bisectors

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Constructing an angle bisector

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Constructing
Equilateral Triangles

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Constructing an equilateral triangle

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Constructing
a perpendicular to a given point on a line

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Constructing a perpendicular to a given
point on a line segment
Construct the perpendicular
bisector of this segment

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Alternative Construction
Constructing a perpendicular to a given
point on a line segment
Why does it work?

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Constructing
a perpendicular to a given point outside a line

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Construct the perpendicular
bisector of this segment
Constructing a perpendicular from a
given point outside a line segment

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Constructing
an identical triangle to one given

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Constructing an identical triangle
to one given

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Constructing
an identical angle to one given

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Constructing an identical angle and sides
to one given

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Constructing an identical angle to
one given

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Constructing
a parallel line to a given line,
through a given point

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Why does it work?
Constructing a parallel line to a given
line, through a given point

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Alternative Construction
Why does it work?
Constructing a parallel line to a given
line, through a given point

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Circumscribing a triangle

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Circumscribing a triangle
The 3 perpendicular bisectors
of the sides of a triangle are
concurrent.
The point they meet is called
the Circumcentre.
The Circumcentre has the
property of being equidistant
from all three vertices of the
triangle.
For this construction:
We need the intersection of
two perpendicular bisectors
(since all three all concurrent).

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Inscribing a triangle in a circle

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Inscribing a triangle in a circle
The 3 angle bisectors of a
triangle are concurrent.
The point they meet is called
the Incentre.
The Incentre has the
property of being equidistant
from all three sides of the
triangle.
For this construction:
We need the intersection of
two angle bisectors (since all
three all concurrent).

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Dividing
a line into a given number of equal segments

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B
Dividing a line into a given number
of equal segments
A
Suppose we want to divide
AB into 3 equal segments

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Construct:
1. The midpoint of a line segment
2. The perpendicular bisector of a line segment
3. The angle bisector of an acute angle
4. The angle bisector of an obtuse angle
5. An equilateral triangle
6. A triangle with sides: 3 cm, 4 cm and 6 cm
7. A 45° angle
8. A 60° angle
9. A 120° angle
10. The perpendicular to a line segment through a
given point on the line segment
11. The perpendicular to a line segment through a
given point outside the line segment
12. A parallel line to a line segment which passes
through a point outside the line segment

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Constructing
Regular
Hexagons

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Constructing a Regular Hexagon
Why does it work?

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Constructing a Regular Hexagon
Why does it work?

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Constructing a Regular Hexagon
Why does it work?

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Constructing
Regular
Pentagons

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• Start with the circumscribing
circle
• Draw a diameter
• Draw the perpendicular
bisector of that diameter
• Mark its intersection with the
circle
• Bisect the radius as shown
• Draw arc as shown and mark its
intersection with the diameter
• This is the required side length
for a regular pentagon, which is
circumscribed by the circle
Constructing a Regular Pentagon

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Constructing
Regular
Octagons

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Constructing a Regular Octagon

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Constructing
Regular
Decagons

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• To construct a decagon you
need a regular pentagon first
• Bisect one of the sides of the
pentagon
• Use the chord of the new arc
produced to construct a
regular decagon
• You can use this idea to
constuct a dodecagon from a
hexagon
• A 16 – sided regular polygon
using an octagon
• An eicosagon from a decagon
and so on
Constructing a Regular Decagon

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