Appendix -Basic Geometry Concepts
You have read the concepts of angles in school already. The following figure shows examples of angles smaller than 90 degrees.
Geometrical Shapes and Their Angles
The table below lists various geometrical shape and their interior and exterior angle.
| SHAPE | NUMBER OF SIDES | EXTERIOR ANGLE | INTERIOR ANGLE |
|---|---|---|---|
| Triangle | 3 | 360 ÷ 3 = 120° | 60° |
| Square | 4 | 360 ÷ 4 = 90° | 90° |
| Pentagon | 5 | 360 ÷ 5 = 72° | 108° |
| Hexagon | 6 | 360 ÷ 6 = 60° | 120° |
| Octagon | 8 | 360 ÷ 8 = 45° | 135° |
| Decagon | 10 | 360 ÷ 10 = 36° | 144° |
Introduction to Coordinate Geometry
A coordinate plane is like graph paper. The figure below shows one horizontal line in the middle of the graph paper. This horizontal line is called the x-axis.
There is one vertical line in the middle of the graph paper, which is called the y-axis.
The horizontal direction is the X-direction and the vertical direction is the Y-direction. The x-axis and y-axis are perpendicular (right angle) to each other.
The point where the x-axis intersects with the y-axis is called the origin. At the origin, the x-value is “0” and the y-value is “0”.
Therefore, the origin is denoted by (0,0). The first “0” in (0,0) is the x-value and the second “0” is the y-value.
The Coordinate Plane
What is the meaning of (0,0)?
To understand this, we will introduce the concept of coordinates. The numbers (0,0} are the coordinates of the origin. At origin, both x and y equal zero.
On the x-axis, there is a scale that goes from zero at the origin to a higher positive number in the right direction and it goes from zero at the origin to a higher negative number in the left direction.
Similarly, there is a scale on the y-axis that goes from zero to a higher positive number in the up direction and from zero to a higher negative number in the down direction.
The following two figures explain the concepts of coordinate geometry and the quadrants.
The figure below shows a coordinate plane with the x-axis and y-axis and the horizontal lines and vertical lines spaced at a distance of 20. The figure also shows a point on the coordinate plane with coordinates of (60,100) in quadrant-1, (-100,+100) in quadrant-2, (-60,-40) in quadrant-3, and (+20,-40) in quadrant-4.
