LESSON 16
GEOMETRY BASICS
The Study of Shapes and Space
What is Geometry?
Geometry is the branch of mathematics that studies shapes, sizes, positions, and the properties of space. The word comes from the Greek 'geo' (earth) and 'metron' (measure) — it was originally developed to measure land.
Geometry surrounds us everywhere — in architecture, art, engineering, nature, and technology. Understanding its basic building blocks — points, lines, angles, and polygons — gives you the tools to describe and analyze the physical world with precision.
Points, Lines, and Planes
A point is an exact location in space with no size — it is represented by a dot and named with a capital letter. A line is a straight path that extends infinitely in both directions through at least two points. A line segment has two endpoints. A ray starts at one endpoint and extends infinitely in one direction. A plane is a flat surface that extends infinitely in all directions.
Angles
An angle is formed by two rays that share a common endpoint called the vertex. Angles are measured in degrees (°). An acute angle is less than 90°. A right angle is exactly 90°. An obtuse angle is between 90° and 180°. A straight angle is exactly 180°. Two angles that add to 90° are complementary; two that add to 180° are supplementary.
Triangles
A triangle is a polygon with three sides and three angles. The angles of any triangle always add up to 180°. Triangles are classified by their sides: equilateral (all sides equal), isosceles (two sides equal), scalene (no sides equal). They are also classified by angles: acute (all angles < 90°), right (one angle = 90°), obtuse (one angle > 90°).
Polygons
A polygon is a closed figure made of straight line segments. Polygons are named by their number of sides: triangle (3), quadrilateral (4), pentagon (5), hexagon (6), heptagon (7), octagon (8). A regular polygon has all sides equal and all angles equal. The sum of interior angles of any polygon with n sides is (n − 2) × 180°.
Key Facts
Euclid's 'Elements', written around 300 BCE, is one of the most influential math textbooks ever written. Its logical approach to geometry shaped mathematics for over 2,000 years.
A circle is not a polygon — it has no straight sides. But it is one of the most important shapes in geometry, defined as all points equidistant from a center.
Honeybees build hexagonal cells in their hives because regular hexagons tile a plane perfectly and use the least material to enclose the most space.
The sum of exterior angles of any convex polygon is always 360°, regardless of the number of sides. Walk around any polygon and you turn a total of one full revolution.