Oh yes, the humble **triangle**, we take it for granted.

Its shape has been used by Egyptian kings, musicians and in warning signs, to name just a few of its many uses!

There are lots of **properties** (facts) about triangles that people have learned over the centuries, and now it is your turn.

** Special Triangles**

From left to right:

An **equilateral** has 3 equal sides

An **isosceles** has 2 equal sides

A **scalene** has no equal sides.

We need to look out for the markings on these triangles, as these tell us which **type of triangle **we are looking at.

We also need to remember the rules about **angles** in each type of triangle:

**All three angles** in an **equilateral** are **equal**.

The two angles at the **base **of an **isosceles** are **equal.**

**All three angles **in a **scalene** are **different.**

Finally, any triangle containing a 90 degree angle is called a right-angled triangle.

Right-angled triangles can be scalene or isosceles, but not equilateral.

**A Key Triangle Fact:**

**Angles in a triangle always add up to 180°.**

Using this knowledge, we can find missing angles in a triangle.

Let's look at how we can do this now.

**e.g. What are the value of angles a and b in the triangle below? **

From the markings on these triangles, we can see this is an **isosceles triangle**.

As a result, we know that the base angles must be **the same**.

Therefore, b = 70º

Finally, angles in a triangle add to 180º, so angle a = 180 - 70 - 70 = 40º

**e.g. What is the value of angle c in the diagram below? **

Here, we have been asked to find an angle that is **external** to the triangle.

We need to put two rules we know together here - if we extend the base of the triangle we have a straight line.

What facts do we know about straight lines?

The angles on a straight line will also **add up to 180°**, so we can use this fact to find the missing exterior angle.

So angle c = 180 - 45 = 135º

Right then, let's put what we know into action now!

In this activity, we will use the key fact, that angles in a triangle always add to 180°, to find the value of unknown angles in triangles, identify triangles accurately and solve problems involving triangles.