# 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

**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:

- Polygons and its types
- Measures of the Exterior Angles of a Polygon
- Rectangle, Square, Rhombus, Parallelogram
- Some Special Parallelograms
- Basic terms and definitions
- Pairs of Angles
- Parallel lines and a transversal
- Lines parallel to the same line and Angle Sum Property
- Properties of triangles
- Angle Sum Property of a Triangle
- Inequalities in a triangle
- Theorem – Angle opposite to equal sides of an isosceles triangle are equal
- Angle sum property of a quadrilateral
- Types of quadrilateral
- Properties of Parallelograms
- MidPoint Theorem
- Rhombus
- Kite – Quadrilaterals
- Area of 2D Shapes
- Figures on the same base and between the same parallels
- Circles and its Related Terms
- Circle Theorems
- Theorem – There is one and only one circle passing through three given non-collinear points
- Theorem – The sum of opposite angles of a cyclic quadrilateral is 180°
- Inscribed Shapes in a Circle
- Basic Construction
- Construction of Triangles
- Construction of a Quadrilateral
- Euclid’s Definitions, Axioms, and Postulates
- Equivalent version of Euclid’s Fifth postulate
- Euclid’s Division Algorithm
- Properties of Triangles
- Construction of Similar Triangles
- Similar Triangles
- Pythagoras Theorem and it’s Converse
- Thales’s Theorem
- Criteria for Similarity of Triangles
- 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:

- Visualizing Solid Shapes
- Mapping Space Around Us
- Cartesian Coordinate System
- Cartesian Plane
- Coordinate Geometry
- Distance formula
- Section formula
- Mid-point Formula
- Area of a Triangle
- Tangent to a circle
- Tangent at any point of a circle is perpendicular to the radius through the point of contact
- Number of Tangents from a point on a circle
- Lengths of tangents drawn from an external point to a circle are equal
- Division of Line Segment in Given Ratio
- Construction of tangents to a circle
- Perimeter of circular figures, Areas of sector and segment of a circle & Areas of combination of plane figures
- Coordinate Axes and Coordinate Planes in 3D
- Distance Formula & Section Formula
- Slope of a Straight Line
- Introduction to Two-Variable Linear Equations in Straight Lines
- Forms of Two-Variable Linear Equations of a line
- Point-slope Form
- Slope-Intercept Form of Straight Lines
- Writing Slope-Intercept Equations
- Standard Form of a Straight Line
- x-intercepts and y-intercepts of a Line
- Graphing slope-intercept equations
- Direction Cosines and Direction Ratios of a Line
- Equation of a Line in 3D
- Angle between two lines
- Shortest Distance Between Two Lines in 3D Space
- Points, Lines, and Planes
- Linear Programming
- Graphical Solution of Linear Programming Problems