Geometry Assignment Help / Geometry Homework Help
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Points and Lines
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Angles- types and relationships
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Parallel lines, transversal
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Complementary/supplementary
angles
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Graphing linear/non-linear
equations
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Graph/slope of lines
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Graphing solutions of
inequalities
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Relation between objects in space
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Planar cross-sections;
perpendicular lines/planes
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Pythagorean Theorem
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Trigonometric ratios,
Pythagorean triples
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Basic constructions
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Angles of triangles and
polygons
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Special right triangles
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Triangle congruence
relationships
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Congruence, Similarity,
triangle inequality theorem
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Isosceles triangle theorem
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Similar triangles-
proportional reasoning
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Properties of
quadrilaterals
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Properties of geometric
figures
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Properties of 2-d and 3-d
figures
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Circles, parallel lines cut
by a transversal
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Inductive/deductive
reasoning
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Properties of
inscribed/circumscribed polygons of circles
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Geometric proofs
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Formal/informal proofs
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Definitions, postulates,
reasoning, theorems
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Measurements of geometric
figures and composite figures
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Logical reasoning
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Conditional statements
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Formal/informal proofs
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Rectangular coordinate
system
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Perimeters and areas of
Two-Dimensional Polygons
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Volume and Surface Areas of
Three- dimensional Polygons
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Vectors and 3D Geometry
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Sketching and modeling
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Tessellations
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Intersection of a plane
with 3-d figures
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Similarity properties and
transformations
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Coordinate geometry
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Rate, distance, time, angle
measures, arc lengths
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Direct/indirect measures
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Error and magnitude
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Coordinate,
transformational, axiomatic systems
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Compound loci in the
coordinate plane.
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Alternative Coordinates
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Rotations, translations,
reflections
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Planar cross-sections;
perpendicular lines/planes
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Effect of rigid motions on
figures
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Properties of circles
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Polyhedra
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Parabolic functions
(vertex, axis of symmetry)
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Euclidean/non-Euclidean
geometries
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Hyperspace and Warped space
Geometry is a branch in mathematics dealing
with questions of size, shape, space properties and relative positions of
various figures. Geometry has early (recorded) beginning in 2nd
millennium B.C. in ancient Egypt and Mesopotamia.
Geometry arose in the very early cultures as early as 6th century B.C. in the
period of Thales of Miletus.
By the 3rd
century BC; geometry was put into axiomatic form by
Euclid, whose Euclidean
geometry has set good mathematical standards for many centuries.
Mathematicians like Archimedes, Rene Descartes, Euler, Gauss, Lobachevsky,
Bolyai,David Hilbert, Papus Menelaus, Immanuel Kant and Riemann
have introduced ingenious techniques and concepts in geometry.
Being visual in nature, geometry is more accessible than other
parts of mathematics like number theory or algebra.
The
origin of geometry is in the form of practical science which is
related to areas, surveying, volumes and measurements. The noticeable
accomplishments were the formulae for areas (circle, squares, rectangles,
two dimensional figures), lengths, volumes of 3- dimensional objects(spheres,
cubes, cylinders, cuboids),the
Pythagoreans, coordinates by Rene Descartes.
The early geometry was a collection of principles
concerning angles, lengths, areas, shapes and volumes that helped to meet
practical requirements in astronomy, construction and surveying. By the 7th
B.C., it was the Greeks who used geometry to distance of ships
from sea shore and for computing the height of pyramids. By early part of the 17th
century, there were two important developments in geometry, the
first being creation of analytical geometry which was an
important for development of physics and calculus and the second being study of
projective geometry in a systematic way which deals only with
study of points in relation to one another and does not involve measurement or
parallel lines.
Geometry has always created an impact on life.
Geometry is present varied forms in daily life. Since geometry
is related to shapes and volumes, it has specific roles in everything that
humans are related to. The application of geometry is there in
various sectors. One could get a better clarity on the angles, shapes and
patterns with the help of geometry. Advanced applications of
geometry find use in areas like architecture, robotics,
typography, computer graphics and textile layout. Without the understanding of
geometry, the basic understanding of various aspects in
different fields would never have been possible.
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