Åk 6–9
 
English/Русский
3.1 Triangles
A triangle is a many sided figure which has three corners and three sides.  Here is a picture of a triangle illustrated with some important concepts.

This is the triangle ABC.

  • Angle A is called the top angle.
  • Angle B and angle C are called the base angles.
  • The height always starts from the top angel and is at a right angle to the base.

Equilateral Triangle
In an equilateral triangle all the side are equally long.  

AB = BC = AC

All the angles are also equally big.

ΛA = ΛB = ΛC

ΛA = ΛB = ΛC = 60º





Isosceles
If a triangle has two equally longs sides, then it is an isosceles triangle.

AB = AC

The angles at the bottom (those which are connected to the long sides) are called base angles are equally big.

ΛB = ΛC

The upper angle is called the top angle.





Right angled triangle
If an angle of a triangle has a right angle then we called it a right angled triangle. 

The two sides that create the right angle are called legs.  The side which connects the two legs is called the hypotenuse.





Pythagorean Theorem
The sum of the squares of the legs is equal to the square of the hypotenuse. 


leg2 + leg2 = hypotenuse2





Obtuse Triangle
A triangle where one of the angles is obtuse, in other words greater than 90° and less than 180°.





Acute Triangle
A triangle where all the angles are acute, in other words less than 90°.





The Triangle’s Perimeter
The triangle’s perimeter is calculated by adding its three sides.

O = a + b + c





The Area of a Triangle  

A triangle can be thought of as half of a parallelogram.  If the triangle is a right-angled one, then it is half of a rectangle, like the one to the right.

The area of a rectangle is calculated by multiplying the base times the height, and then to get the triangle’s area we divide by 2.

(3.5 · 4.5) ÷ 2 ≈ 7.9 cm2