Geometry

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. Kite – Quadrilaterals
18. Area of 2D Shapes
19. Figures on the same base and between the same parallels
20. Circles and its Related Terms
21. Circle Theorems
22. Theorem – There is one and only one circle passing through three given non-collinear points
23. Theorem – The sum of opposite angles of a cyclic quadrilateral is 180°
24. Basic Construction
25. Construction of a Quadrilateral
26. Euclid’s Definitions, Axioms, and Postulates
27. Equivalent version of Euclid’s Fifth postulate
28. Similar Triangles
29. Pythagoras Theorem and it’s Converse
30. Thales’s Theorem
31. Criteria for Similarity 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. Coordinate Axes and Coordinate Planes in 3D
17. Distance Formula & Section Formula
18. Slope of a Straight Line
19. Introduction to Two-Variable Linear Equations in Straight Lines
20. Forms of Two-Variable Linear Equations of a line
21. Point-slope Form
22. Slope-Intercept Form of Straight Lines
23. Standard Form of a Straight Line
24. x-intercepts and y-intercepts of a Line
25. Graphing slope-intercept equations
26. Direction Cosines and Direction Ratios of a Line
27. Equation of a Line in 3D
28. Angle between two lines
29. Shortest Distance Between Two Lines in 3D Space
30. Points, Lines, and Planes