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Sets of
Points in a Plane
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Line, a half-line and line segment
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The line segment bisector
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Angle, measurement of angles
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Complementary, supplementary,
alternate and vertically opposite angles
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Angle bisector
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Construction of angles; 60°, 30°, 90°
and 45° (degrees)
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Points,
Lines and Planes in Three-Dimensional (3D) Space |
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Position
of two lines in a three-dimensional space |
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Coplanar lines and skew lines
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Line and plane in a three-dimensional space
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Two planes in a
three-dimensional space
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The line of intersection of two planes
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Orthogonality of line and plane
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Orthogonality of two planes
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Orthogonal projection of a point onto a plane
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The distance from a point to a plane
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Angle between a line
and a plane, and angle between two planes |
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Plane
Geometry – Plane Figures |
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Triangles |
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Types of triangles
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Main
properties of triangles
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Congruence of triangles
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Theorems about congruence
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Similarity
of triangles, division of a line segment in a given ratio |
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Similarity criteria of triangles
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Area of a triangle
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Right-angled
Triangle
- The Pythagorean Theorem |
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The
Pythagorean theorem |
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Trigonometric functions of an acute angle defined in a right triangle
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Solving the right triangle |
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Equilateral
and Isosceles Triangle
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Equilateral
triangle
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Isosceles
triangle
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Oblique
or Scalene Triangle |
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Properties and rules
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Perpendicular bisectors,
triangles circumcenter
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Angle bisectors, the center of the triangle’s incircle
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The
median, the centroid of a triangle |
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The altitude of a triangle, orthocenter
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Triangle formulas |
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Similarity and congruence of
triangles use
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Congruence |
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The
sine law (or the sine rule) and the cosine law |
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The
sine law |
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The
sine law examples |
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The
cosine law |
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The
cosine law examples |
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Calculating angles
of an oblique triangle |
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Solving
the oblique triangle - use of the sine law and the cosine law |
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Triangle problems
and solutions |
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Triangle solved problems, examples |
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Triangle solved
problems - A |
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Triangle solved
problems - B |
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Triangle solved
problems - C |
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Triangle solved
problems - D |
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Triangle solved
problems - E |
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Triangle solved
problems - F |
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Quadrilaterals |
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Square
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Rhombus
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Rectangle |
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Parallelogram |
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Kite
or deltoid
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Trapezium
or trapezoid
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Isosceles
trapezoid
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Cyclic quadrilateral |
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Tangential quadrilateral
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Polygons
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Regular
polygons |
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Circle
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Central angle, inscribed angle
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Construction of a tangent
from a point
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Circumference, length of an arc
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Circle and circular sector
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Circular segment
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Annulus and annulus segment |
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Plane figures solved problems,
examples |
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Plane figures solved problems,
examples |
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Plane figures solved problems,
examples - A |
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Plane figures solved problems,
examples - B |
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Plane figures solved problems,
examples - C |
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Plane figures solved problems,
examples - D |
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| Solid
Geometry - Solid Figures |
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Prisms |
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Cube |
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Rectangular
prism - cuboid |
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Right
triangular prism |
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Regular
right triangular prism |
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Regular
right hexagonal prism |
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Pyramids |
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Regular
square pyramid |
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Regular
triangular pyramid |
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Regular
hexagonal pyramid |
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Right
pyramidal frustum |
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Solids
of Revolution |
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Cone |
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Conical
frustum |
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Cylinder |
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Sphere |
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Spherical cap |
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Spherical segment |
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Spherical sector |
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Regular
Polyhedrons |
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Tetrahedron |
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Octahedron |
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Dodecahedron |
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Icosahedron |
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Solid figures solved problems,
examples |
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Solid figures solved problems,
examples |
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Solid figures solved problems,
examples - A |
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Solid figures solved problems,
examples - B |
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Solid figures solved problems,
examples - C |
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Solid figures solved problems,
examples - D |
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Solid figures solved problems,
examples - E |
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Solid figures solved problems,
examples - F |
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Solid figures solved problems,
examples - G |
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| Application
of Trigonometry |
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Right-angled
Triangle
or Right Triangle |
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Trigonometric functions of an acute angle defined in a right triangle
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Solving right triangles |
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Solving right triangles examples |
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Oblique
or Scalene Triangle |
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The
sine law (rule) or the law of sines |
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The cosine
law (rule)
or
the law of
cosines |
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Calculating angles
of an oblique triangle |
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Solving oblique triangles - use of
the sine law and the cosine law |
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Solving oblique triangles examples |
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Mollweide's formulas, the tangent
law (or the tangent rule) and half-angle formulas |
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The tangent law or the tangent rule |
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Half-angle formulas |
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Area of a triangle, the radius of
the circumscribed circle and the radius of the inscribed circle |
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The radius of the circumscribed circle or circumcircle |
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Area of a triangle in terms of the inscribed circle or incircle |
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The
radius of the inscribed circle |
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Oblique or scalene triangle
examples |
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Application of Trigonometry in Plane Geometry, Solid Geometry,
Plane Surveying and Physics |
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Applications
of trigonometry in Plane Geometry |
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The parallelogram - Area of a
parallelogram |
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Trapezoid or trapezium |
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The area of a trapezoid given its four sides
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The area of the trapezoid given two parallel sides
(bases) and angles at the ends of the longer base |
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Diagonals of a trapezoid,
determining the diagonals of the trapezoid given its four sides |
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Applications
of trigonometry in Solid Geometry |
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Right pyramid |
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Right pyramids, examples |
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Sections of solids |
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Sections of solids, examples |
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Oblique prism |
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Oblique Pyramid |
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Applications
of Trigonometry in Geodesy (or Plane Surveying) and Physics |
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Applications in geodesy or plane
surveying |
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Applications in physics |
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An example of using trigonometry in
optics |
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Volume
and Surface Area of Solids of Revolution, Guldin’s Rules |
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| Copyright
© 2004 - 2012, Nabla Ltd. All rights reserved. |