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Geometry Quick Study Guide - FREE Geometry Background and Triangles chapters in the trial version -
Boost Your grades with this illustrated quick-study guide. You will use it from college to graduate school and beyond. FREE Geometry Background and Triangles chapters in the trial version.
Features
- Clear and concise explanations
- Difficult concepts are explained in simple terms
- Illustrated with graphs and diagrams
Table of Contents
Geometry Background
- Euclidean Geometry
- Euclidean Space
- Line
- Line Segment
- Incidence of planes and lines
- Euclidean Distance
- One-dimensional distance
- Two-dimensional distance
- Three-dimensional distance
- Postulate
- The Plane Areas of Mathematics
- Translation
- Translational Symmetry
- Similarity
Triangles
- Triangle
- Types of triangles
- Points, lines and circles associated with a triangle
- Computing the area of a triangle
- Using vectors
- Using trigonometry
- Using coordinates
- Using Heron's formula
- Ceva's Theorem
- Heron's Formula
- Equilateral Triangle
- Right Angle
- Pythagorean Theorem
- Pythagorean Triple
- Heronian Triangle
- Triangle Inequality
- Pedoe's Inequality
- Similar triangles
Parallel Lines
- Congruence
- Parallel Postulate
Polygons
- Convex polygon
- Internal Angle
- Diagonal
- Perimeter
- Quadrilateral
- Isosceles Trapezoid
- Parallelogram
- Kite
- Rhombus, Rhomboid
- Rectangle
- Square
- Cyclic Quadrilateral, Brahmagupta's formula
- Tangential Quadrilateral
- Star Polygon
Circles
- Analytic results
- Properties
- Calculating the parameters
- Area of a Disk
- Circular Sector
- Circular Segment
- Circumference
- Nine-point Circle
Transformational Geometry
- Scaling
- Rotation,
- Euler's Formula,
- Rotation Matrix,
- Quaternions and Spatial Rotation
- Reflection
- Coordinate Rotations and Reflections
- Linear Map
Solid Geometry
- Dihedral angle and Solid angle
- The Cube
- Cuboid
- Hypercube Graph
- Parallelepiped
- Prisms
- The Tetrahedron and Pyramid
- Octahedron, Dodecahedron, Icosahedron
- Cones and Cylinders
- The Sphere and Spheroid,
- Quadrics:
- Ellipsoid
- Paraboloid
- Hyperboloid
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