Eugene is a qualified control/instrumentation engineer Bsc (Eng) and has worked as a developer of electronics & software for SCADA systems.
David Wilson, maths lesson resource creator, former maths teacher, and current owner of www.doingmaths.co.uk
What Is a Triangle?
A triangle is a polygon with three sides.
So what do we mean by polygons?
Polygons are plane shapes with three or more straight sides. "Plane" just means they're flat and two-dimensional like a sheet of paper and not solid like a ball. Other examples of polygons are squares, pentagons, hexagons and octagons. We get the word polygon from the Greek word polús meaning "many" and gōnía meaning "corner" or "angle." So polygon just means "many corners." We can't have a shape with only two straight sides, so a triangle is the simplest possible polygon, having three sides.
What Are Angles?
An angle is just a measurement of how pointy the space is between two lines that join at a point. If the lines slope move apart or diverge gradually, the angle is small and if the lines diverge quicker, the angle is bigger. When the angle is square, like the corner of a rectangle or square, we call this a right angle and it measures 90 degrees.
The Symbol for Degrees
Angles are measured in degrees. Degrees can be written using the symbol º. So, 45º means 45 degrees.
Basic Facts About Triangles
- A triangle is a polygon with three sides.
- All the internal angles add up to a total of 180 degrees.
- The angle between two sides can be anything from greater than 0 to less than 180 degrees.
- The angle between two sides can't be 0 or 180 degrees, because the triangle would then become three straight lines superimposed on each other (These are called degenerate triangles).
- Similar triangles have the same angles, but different length sides.
The Angles of A Triangle Add up to 180 Degrees
If we measure the three angles of a triangle and add them all up, the answer is always 180 degrees.
So we could have 100º + 40º + 40º = 180º
or 120º + 10º + 50º = 180º
If the angles are all the same, we have an equilateral triangle.
60º + 60º + 60º = 180º
What Are the Different Types of Triangles?
We can classify a triangle in two different ways
- By the length of the triangle's sides
- By the angles of the triangle's corners
|Type of Triangle by Lengths of Sides||Description|
An isosceles triangle has two sides of equal length, and one side that is either longer or shorter than the equal sides.
All sides and angles are equal in length and degree.
All sides and angles are of different lengths and degrees.
|Type of Triangle by Internal Angle||Description|
Right (right angled)
One angle is 90 degrees.
Each of the three angles measure less than 90 degrees.
One angle is greater than 90 degrees.
Similar triangles are triangles that have the same angles, but different length sides. If we divide the lengths of one triangle by the corresponding lengths of the other triangle, the ratio is always the same.
So lets say one triangle has sides of length 2, 3 and 4 units.
The second triangle has sides of length 8, 12 and 16 units long.
If we divide the sides we get 8/2 = 12/3 = 16/4 = 4
So the ratio of the sides is 4.
What Is the Triangle Inequality Theorem?
This states that the sum of any two sides of a triangle must be greater than or equal to the remaining side.
This content is accurate and true to the best of the author’s knowledge and is not meant to substitute for formal and individualized advice from a qualified professional.
© 2022 Eugene Brennan