Welcome
Welcome to geometry!
The word geometry comes from two Greek words: geo (earth) and metria (measurement). Thousands of years ago, people invented geometry to measure land, build buildings, and understand the shapes they saw all around them.
Today you are going to learn the basic building blocks of geometry — points, lines, angles, shapes, and symmetry.
Let's get started!
Points, Lines, Rays, and Segments
The Building Blocks
Here are the four building blocks of geometry:
- A point is an exact location. We draw it as a dot and label it with a letter like A.
- A line goes on forever in both directions. It has arrows on both ends to show it never stops.
- A ray starts at a point and goes on forever in one direction. Think of a flashlight beam — it starts somewhere and shines outward.
- A line segment has two endpoints. It is the part of a line between two points — like the edge of your desk.
Lines vs. Rays
Your Turn
Think about the difference between a line and a ray.
What is an Angle?
Angles
An angle is formed when two rays meet at a point. That meeting point is called the vertex.
There are four main types of angles:
- Acute angle — less than 90 degrees. It looks sharp and pointy, like the tip of a pizza slice.
- Right angle — exactly 90 degrees. It makes a perfect square corner, like the corner of a book or a door frame.
- Obtuse angle — more than 90 degrees but less than 180. It looks wide and lazy, like leaning back in a chair.
- Straight angle — exactly 180 degrees. It looks like a flat line.
Here is a trick: if the angle fits inside a square corner, it is acute. If it is bigger than a square corner, it is obtuse.
Name That Angle
Your Turn
Imagine picking up a book and opening it partway, so the front and back covers make a V shape.
What is a Polygon?
Polygons
A polygon is a closed shape made of straight sides. The sides connect end to end with no gaps.
Here are the most common polygons:
- Triangle — 3 sides (tri = three)
- Quadrilateral — 4 sides (quad = four). Squares and rectangles are special quadrilaterals!
- Pentagon — 5 sides (penta = five)
- Hexagon — 6 sides (hexa = six). Honeycombs are made of hexagons!
- Octagon — 8 sides (octa = eight)
Notice the pattern? The name tells you how many sides the shape has.
Name That Shape
Your Turn
Think about a stop sign. It has 8 sides.
Lines of Symmetry
Symmetry
A shape has symmetry if you can fold it in half and both sides match exactly.
The fold line is called a line of symmetry.
Some shapes have many lines of symmetry, and some have none:
- A heart has 1 line of symmetry — fold it down the middle vertically.
- A square has 4 lines of symmetry — vertical, horizontal, and both diagonals.
- A circle has infinite lines of symmetry — you can fold it through the center in any direction!
- The letter F has 0 lines of symmetry — no matter how you fold it, the two sides do not match.
Try this at home: cut a shape out of paper and fold it. If both halves match perfectly, the fold is a line of symmetry!
Finding Symmetry
Your Turn
Think about the capital letter A.
What is Perimeter?
Perimeter
The perimeter of a shape is the total distance around the outside.
Imagine walking around the edge of a soccer field. The distance you walk is the perimeter.
To find the perimeter, add up the lengths of all the sides.
Rectangle shortcut:
A rectangle has two long sides (length) and two short sides (width).
So the perimeter = length + length + width + width, which is the same as:
Perimeter = 2 x length + 2 x width
For example, a rectangle that is 6 meters long and 3 meters wide has a perimeter of:
2 x 6 + 2 x 3 = 12 + 6 = 18 meters
Calculate the Perimeter
Your Turn
A rectangular garden is 8 meters long and 5 meters wide.