Download Geometrical shapes - Colegio Cardenal Newman

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Geometrical shapes
The main geometrical shapes used in graphics are triangles, quadrilaterals, regular
polygons, circles and ellipses. Click on the shapes below to see how to draw them.
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Here are some guidelines to help you when drawing these shapes.
Polygons are shapes with three or more straight sides.
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Regular polygons are polygons with all sides equal and all angles equal. Regular
polygons with five sides are called pentagons, regular polygons with six sides are
called hexagons, and regular polygons with eight sides are called octagons.
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Triangles are a type of polygon with three sides, with three angles adding up to
180°. There are three main types of triangle. Equilateral triangles have sides of equal
size and all angles are 60°. Right-angled triangles have one 90° angle. Isosceles
triangles have two sides and two angles that are equal.
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Quadrilaterals are a type of polygon with four sides, and four angles adding up to
360°. A quadrilateral where all the angles are 90°, the opposite sides are equal and
the diagonals are of equal length is called a rectangle. A rectangle where all four
sides are of equal length is called a square.
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A quadrilateral where opposite sides are the same length, but none of the angles are
90°, is called a parallelogram. A parallelogram where all four sides are the same
length is called a rhombus.
Construct a regular octagon using only a ruler and compasses:
1. Draw a square and then draw diagonal lines from opposite
corners so that you can locate the centre of the square.
2. Place the point of your compasses in the top left corner of
your square and open them out until the pencil touches the
centre of the square (marked by the thick green line).
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3. With your point still in the top left corner, draw two arcs, one
crossing the top of the square and one crossing the left of the
square (marked by red lines).
4. Repeat step 3 another 3 times, once for each of the remaining
corners of the square. When you have completed this step,
you should have EIGHT arcs, two per side (marked by red
lines).
5. Join up the points where the arcs cross the sides of the square
(marked by the blue lines).
6. Finally, rub out all construction lines and you have a perfect
regular octagon!
Triangular Structures:
A triangle is a plane figure having three sides and three angles. The sum of the angles in
any triangle is always 180º.
The triangle is a simple shape but when it is made from steel girders it is strong and rigid.
This is why so many roof trusses, bridges and cranes are built up from series od steel
triangles. It is one of the most important and useful shapes used in building constructions.
Types of triangles: There are six different shapes of triangles. Three of these are named
by the length of their sides and three by the magnitude of their angles:
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Equilateral: triangles have three equal sides and three equal angles. Fig. 4.1
Isosceles: triangles have two equal sides and two equal angles. Fig. 4.2
Scalene: triangles have three unequal sides and three unequal angles. Fig. 4.3
Acute-angled: triangles have three acute angles. Fig. 4.4
Right-angled: triangles have one right angle and two acute angles. Fig. 4.5
Obtuse-angled: triangles have one obtuse angle and two acute angles. Fig. 4.6
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Properties of Triangles: Triangles have separate names for their parts as shown in Fig.
The vertex or apex, is the point of the angle opposite to
the base.
The altitude is the perpendicular height from the base to
the vertex.
The hypotenuse is the longest side in a right-angle
triangle and is always opposite to the right angle.
A median is a line drawn from any angle to the centre of the
opposite side.
The perimeter is the sum of the lengths of the tree sides.
Similar triangles have corresponding angles of equal magnitude,
even though the lengths of the corresponding side are different.
Constructing Triangles
Equilateral triangles
Given the length of side (fig. 4:10)
1. Draw a line AB, 60 mm in length
2. Using A and B as centres, and AB radius, draw
two arcs intersecting at C. Join AC and BC.
Given the length of the altitude (fig. 4:11)
1. Draw the base AB, any length. Construct the
perpendicular bisector.
2. Mark off the point C 60 mm above the baseline.
3. Construct a 30º angle at DCB. Repeat the
construction at DCA.
Equilateral triangles
Given the length of side (fig. 4:10)
1. Draw a line AB, 60 mm in length
2. Using A and B as centres, and AB radius, draw
two arcs intersecting at C. Join AC and BC.
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Equilateral triangles
Given the length of the altitude (fig. 4:11)
1. Draw the base AB, any length. Construct the
perpendicular bisector.
2. Mark off the point C 60 mm above the baseline.
3. Construct a 30º angle at DCB. Repeat the
construction at DCA.
Isosceles triangles
Given the base and the vertex angle
1. Draw the base AB, 40 mm long, and its
perpendicular bisector.
2. Draw a semicircle CD, With A as centre and
half the base as radius.
3. Draw the line AE, forming a 40º angle with the
line CA.
4. Bisect the angle EAD to cut the perpendicular
at F.
5. Join B to F to complete the triangle.
Scalene (and Acute-angle) triangles
Given the lengths of the three sides
1. Draw AB, equal in length to line
2. Using A as centre and a radius equal to the
length of line 3, draw an arc at C.
3. Using B as centre and line 2 as radius, draw a
second arc cutting the first at C. Join A and B to
C.
Points to Remember:
Any triangle can be constructed providing three properties are known. These may be any of
the following:
1. The length of the three sides
2. The lengths of two sides and the size of their included angle.
3. The length of one side and the size of two angles.
Circles and ellipses

Circles are perfectly round and have the same diameter (the distance from side to
side and top to bottom, through the middle of the circle. To draw a circle accurately,
use a pair of compasses. Set the compasses to the radius of the circle (the radius is
distance between the middle and the outside, it is half the diameter).

Ellipses look like stretched circles. The diameter is not the same from top to bottom
and right to left. These diameters are called the major axis and minor axis (the
major axis is the longer one, the minor axis the shorter one). Here's how to draw an
ellipse by construction:
1. Draw the major and minor axes. Draw two circles with diameters equal to the
major and minor axes.
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2. Divide up the circles into 12 equal segments
3. Where the segment lines cross the smaller circle, draw a horizontal line.
Where they cross the larger circle, draw a vertical line.
4. Each intersection point between vertical and horizontal lines is a point on the
curve of your ellipse.
5. Join the intersection points with a freehand curve.
Geometrical solids:
The main geometrical solids used in representing graphic products are the cube, cuboid,
triangular prism, hexagonal prism, square-based pyramid, cylinder and cone. Click on the
solids below to see how to draw them.
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Here are some guidelines to help you when drawing these solids.
Cubes have six faces. All faces are square, with equal-length sides and angles of 90°.
Cuboids have six rectangular faces. The opposite faces are equal and all the angles are
right angles at 90°.
Hexagonal prisms have eight sides. The two ends are hexagons. The six sides are square
or rectangular.
Cylinders have two ends that are circles and one continuous face around the outside. If
this was opened out the flat the side of a cylinder would be a large rectangle.
Triangular prisms have five sides. The two ends are triangles. The sides are square or
rectangular.
Cones have a base that is a circle. One face goes all round and narrows towards a point at
the top.
Pyramids are usually square-based. This square-based pyramid has five faces. The base of
is a square. The four sides are triangles, which all meet at a point at the top. There are also
triangle-based (with a triangle base and three sides) and hexagon-based pyramids (with a
hexagon base and six sides), among other variations.
Surface developments
A surface development - also called a net - is a shape
cut from sheet material to make a 3D form.
Developments can be used for any shape: cube, cuboid,
prism, pyramid, cylinder or cone. The diagram below
shows the development for a cube.
If the 3D form is made from board, tags have to be
added to show where it will be glued together.
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Signs and symbols
Signs and symbols are another
kind of drawing used to convey
information. Signs and symbols
stand in for words. Examples
include road signs and information
signs at airports and railway
stations.
Car drivers will know what most of
the signs below mean without any
need for written instruction. How
many of them do you know?