Triangles:
Equilateral Triangle
 Three equal sides
 Three equal angles, always 60°
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Isosceles Triangle
 Two equal sides
 Two equal angles
Scalene Triangle
 No equal sides
 No equal angles
Angles:
Acute Triangle
 All angles are less than 90°
Right Triangle
 Has a right angle (90°)
Obtuse Triangle
 Has an angle more than 90°
Quadrilaterals:
 Quadrilateral just means "four sides

“Any four-sided shape is a Quadrilateral. But
the sides have to be straight, and it has to be2dimensional.
Pentagons:
 A pentagon has 5 straight sides
 A pentagon is a 5-sided polygon (a flat shape
with straight sides)
 If all angles are equal and all sides are equal,
then it is regular, otherwise it is irregular
 A pentagon has 5 straight lines. The shape
must also be closed (all the lines connect up)
Hexagons:
 So long as it has 6 straight sides, it is still a
hexagon
 If all angles are equal and all sides are equal,
then it is regular, otherwise it is irregular

A hexagon has 6 straight lines. The shape
must also be closed (all the lines connect up).
Polyhedrons
 Dice are Polyhedrons, there made up of
polygon joined together
 A cube is a basic polyhedron made out of six
sides and it is sometimes called a hexahedrons
 Tetrahedron tetra =4 made up of 3 triangles
and are joined at each vertex a regular
Tetrahedron is made up of equilateral triangles
 An octahedron is you can make another
regular by adding another 5 sides to it
 When u put 12 more together you get a
dodecahedrons
 5 equilateral triangles in each vertex called a
icosahedrons (its 20 sides)
 Polyhedrons are sometimes called the dice of
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
the gods.
There are many different Polyhedron

A prism is a solid with 2 congrowing bases the
sides are parrleograms we name them by the
shapes of the bases
 A cube has
Transformation is movement of shapes in to and 3D
shapes
There are 3 different types of basic transformation,
translation, rotation, and reflection
U can see symmetry all over the place the natural work
is ordered in symmetric patterns.
 Translation is where a shape is moved from
one place to another it is described by
direction and distance
 Rotion is when u turn a ahpe in a single shape
like a clock
 A reflection is when u flip a shape over a line
Phi ( = 1.618033988749895...), most often pronounced
fi like "fly," is simply an irrational number like pi (p =
3.14159265358979...), but one with many unusual
mathematical properties. Unlike pi, which is a
transcendental number, phi is the solution to a
quadratic equation. Phi is the basis for the Golden
Section, Ratio or Mean. The ratio, or proportion,
determined by Phi (1.618 ...) was known to the Greeks
as the "dividing a line in the extreme and mean ratio"
and to Renaissance artists as the "Divine Proportion” It
is also called the Golden Section, Golden Ratio and the
Golden Mean. Phi, like Pi, is a ratio defined by a
geometric construction. Phi with an upper case "P" is
1.618 0339 887 ..., while phi with a lower case "p" is
0.6180339887, the reciprocal of Phi and also Phi minus
1. What makes phi even more unusual is that it can be
derived in many ways and shows up in relationships
throughout the universe.
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http://www.goldennumber.net
Building, creating structures is called architecture.
architect follow 3 basic principles, structurally sound,
design for function ment to served, aesthetics is the
way building looks and feels. Ancient people made
structures were made from stone and brick, clay,
boulders. Classis renaissance (mathematic proportions,
arches, domes, classic columns), medieval (gothic,
Tudor, Romanesque), 1900s became modern
architectures (simple and wacky imaginations).
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