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  • Last Updated :30 May, 2022
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Geometry is the branch of mathematics that deals with the forms, angles, measurements, and proportions of ordinary objects. There are two-dimensional forms and three-dimensional shapes in Euclidean geometry. Flat shapes are two shapes in plane geometry that include triangles, squares, rectangles, and circles. 3D forms such as a square, cuboid, cone, and so on are also known as solids in solid geometry. The fundamental geometry is based on points, lines, and planes, as described in coordinate geometry.

The various forms of shapes in geometry help us understand the shapes we see in our daily lives. We can measure the field, circumference, and volume of shapes using geometric principles.

Table of Content

  1. Plane Geometry
  2. Solid Geometry

Plane Geometry

Plane geometry is concerned with platforms that can be drawn on paper. Lines, circles, and triangles in two dimensions are examples. Plane geometry is another name for two-dimensional geometry. All two-dimensional figures have only two dimensions: length and width. It does not take into account the depth of the shapes. Plane figures have squares, triangles, rectangles, circles, and so on. Any of the most essential terms in plane geometry are described here in the below articles:

  1. Polygons and its types
  2. Measures of the Exterior Angles of a Polygon
  3. Rectangle, Square, Rhombus, Parallelogram
  4. Some Special Parallelograms
  5. Basic terms and definitions
  6. Pairs of Angles
  7. Parallel lines and a transversal
  8. Lines parallel to the same line and Angle Sum Property
  9. Properties of triangles
  10. Angle Sum Property of a Triangle
  11. Inequalities in a triangle
  12. Theorem – Angle opposite to equal sides of an isosceles triangle are equal
  13. Angle sum property of a quadrilateral
  14. Types of quadrilateral
  15. Properties of Parallelograms
  16. MidPoint Theorem
  17. Rhombus
  18. Kite – Quadrilaterals
  19. Area of 2D Shapes
  20. Figures on the same base and between the same parallels
  21. Circles and its Related Terms
  22. Circle Theorems
  23. Theorem – There is one and only one circle passing through three given non-collinear points
  24. Theorem – The sum of opposite angles of a cyclic quadrilateral is 180°
  25. Inscribed Shapes in a Circle
  26. Basic Construction
  27. Construction of Triangles
  28. Construction of a Quadrilateral
  29. Euclid’s Definitions, Axioms, and Postulates
  30. Equivalent version of Euclid’s Fifth postulate
  31. Euclid’s Division Algorithm
  32. Properties of Triangles
  33. Construction of Similar Triangles
  34. Similar Triangles
  35. Pythagoras Theorem and it’s Converse
  36. Thales’s Theorem
  37. Criteria for Similarity of Triangles
  38. Congruence of Triangles

Solid Geometry

Solid geometry is concerned with three-dimensional structures such as cubes, prisms, cylinders, and spheres. It is concerned with the figure’s three dimensions, which are length, width, and height. However, certain solids do not have faces (e.g. sphere). The analysis of three dimensions in Euclidean space is known as solid geometry. The structures of our environment are three-dimensional. Both three-dimensional shapes are created by rotating two-dimensional shapes. Faces, corners, and vertices are essential characteristics of 3D forms. Examine these words in depth for various geometric forms here in the following articles:

  1. Visualizing Solid Shapes
  2. Mapping Space Around Us
  3. Cartesian Coordinate System
  4. Cartesian Plane
  5. Coordinate Geometry
  6. Distance formula
  7. Section formula
  8. Mid-point Formula
  9. Area of a Triangle
  10. Tangent to a circle
  11. Tangent at any point of a circle is perpendicular to the radius through the point of contact
  12. Number of Tangents from a point on a circle
  13. Lengths of tangents drawn from an external point to a circle are equal
  14. Division of Line Segment in Given Ratio
  15. Construction of tangents to a circle
  16. Perimeter of circular figures, Areas of sector and segment of a circle & Areas of combination of plane figures
  17. Coordinate Axes and Coordinate Planes in 3D
  18. Distance Formula & Section Formula
  19. Slope of a Straight Line
  20. Introduction to Two-Variable Linear Equations in Straight Lines
  21. Forms of Two-Variable Linear Equations of a line
  22. Point-slope Form
  23. Slope-Intercept Form of Straight Lines
  24. Writing Slope-Intercept Equations
  25. Standard Form of a Straight Line
  26. x-intercepts and y-intercepts of a Line
  27. Graphing slope-intercept equations
  28. Direction Cosines and Direction Ratios of a Line
  29. Equation of a Line in 3D
  30. Angle between two lines
  31. Shortest Distance Between Two Lines in 3D Space
  32. Points, Lines, and Planes
  33. Linear Programming
  34. Graphical Solution of Linear Programming Problems

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