Art & Design - 3ºESO
Unit 7
Francisco Rañal Loureiro (revised by C. Pigott)
- Analysis of Basic Forms
7.1. Triangles
Triangles are flat figures formed by three non-aligned
points (called vertices) connected by three segments (called
sides). Vertices are lettered using capitals, while their
corresponding opposite side is named with the same letter but in
lower case.
The sum of the three angles of a triangle is 180º.
The base of a triangle is the side on which it is standing.
The three altitudes of a triangle are the three perpendicular
distances from each vertex to its opposite side.
The medians of a triangle are the three lines connecting
each vertex and the midpoint of the opposite side.
7.1.1. Clasification
Depending on the sides:
- Equilateral: all sides are of equal length and all
angles are of equal size (60º).
- Isosceles: two sides are of equal length and two
angles are of equal size.
- Scalene: all sides are of different lengths and all
angles are of different sizes.
Depending on the angles:
- Right-angle triangle: one angle is a right angle.
- Acute-angle triangle: all angles are acute.
- Obtuse-angle triangle: one of the three angles is
obtuse.
Depending on the lines:
- Straight-sided: the three sides are straight lines.
- Curve-sided: the three sides are curves.
- Mixed-sided: one or two sides are curves.
7.1.2. Centres
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Circumcentre: the centre of the circumference
that circumscribes the triangle (touches its three
vertices). It is the point where the perpendicular
bisectors of each side intersect.
Incentre: the centre of the circumference that
inscribes the triangle (is tangential to each side of
the triangle). It is the point where the three angle
bisectors intersect.
Orthocentre: the common point of the three
altitudes.
Barycentre: the common point of the three
medians.
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Art & Design - 3ºESO
Francisco Rañal Loureiro (revised by C. Pigott)
7.2. Quadrilaterals
Quadrilaterals are polygons that have four sides and four
angles.
Vertices are lettered using consecutive capitals (A,B,C,D)
while sides are named with the same letters but in lower case.
The sum of the four angles of a quadrilateral gives 360º.
Diagonals are the segments that join two opposite vertices
of a figure. A quadrilateral has two diagonals.
7.2.1. Clasification
- Trapezoid: Quadrilateral with no parallel sides.
- Kite: has two sets of adjacent sides equal in
length.
- Trapezium: Quadrilateral with only two parallel sides
called bases. Its altitude is the distance between both.
- Right-angle trapezium: it has two right angles.
- Isosceles trapezium: the pair of non-parallel
opposite sides are equal in length.
- Scalene trapezium: it has no equal sides.
- Parallelogram: Quadrilateral in which both pairs of
opposite sides are parallel and of equal length, and the
opposite angles are equal.
- Square: all four sides are of equal length and the
two sets of opposing, parallel sides are
perpendicular to each other.
- Rectangle: the two sets of opposing, parallel
sides are perpendicular to each other.
- Rhombus: has four equal sides and opposing
angles equal in size. Both diagonals are
perpendicular.
- Rhomboid: has two sets of opposing, parallel
sides non perpendicular to each other.
7.3. Circumference and circle
7.3.1. Circumference
It is the flat, closed curve whose points are equidistant from
a fixed point called centre.
Radius: is the distance from the centre to any
point on the circumference. (The plural of radius is radii).
- Arc: part of the circumference.
- Semicircumference:One-half the circumference.
- Central angle: it is defined by any two radii.
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Art & Design - 3ºESO
Francisco Rañal Loureiro (revised by C. Pigott)
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Chord: a segment with each end touching the
circumference.
Diameter: the longest possible chord of a
circumference passing through its centre. It is
twice the radius.
Secant: straight line that intersects a
circumference in two points.
Tangent: a straight line that touches a
circumference in only one point and does not
cross or intersect it.
7.3.2. Circle
It is the area enclosed by a circumference. A circumference
is the perimeter of a circle.
- Semicircle: half a circle.
- Quadrant: quarter of a circle.
- Circular crown: surface delimited by two
concentric circumferences.
- Circular segment: portion of a circle delimited by
an arc and its corresponding chord.
- Circular girdle: Portion of a circle delimited by
two parallel chords.
- Circular sector: Portion of a circle delimited by
two radii and the corresponding arc.
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