Subject: Geometry

# Triangles

The Breakdown
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## The basics of naming triangles

A triangle can be named with the three letters that signify its vertices, although some textbooks name triangles with a Roman numeral placed in the centre.

We classify triangles according to:

- Equality of the length of their sides
- Angle size

## Triangles according to the equality of the length of their sides

### Scalene

In a scalene triangle no length is congruent with any other length and therefore, no angle is congruent with any other angle.

### Isosceles

An isosceles triangle has at least two sides of equal length. These sides are called the legs. The other is called the base. They are typically drawn with the base on the bottom.

### Equilateral

A equilateral (also called equiangular) triangle has three congruent sides, and therefore three congruent angles. By definition, an equilateral triangle is also an isosceles triangle.

**Figure 1: Example of scalene, isosceles and equilateral triangles**

## Triangles according to angle size

### Right

A right triangle has one right angle. The side opposite the right angle is called the hypotenuse.

### Obtuse

An obtuse triangle has one obtuse angle.

### Acute

Acute triangles have three acute angles.

**Figure 2: Example of right, obtuse and acute triangles**

## Triangles according to the combination of both length and angle size

Some triangles will have a combination of these qualities. For instance, we might see a right isosceles, with a right angle where the legs meet. If you were to measure the lengths and angles of the triangles in the above picture, you would see that they are all scalene – a right scalene, an obtuse scalene, an acute scalene. Have a look at the next picture.

**Figure 3: Example of triangles classified according to both length and angle size**

Have a look at the picture below. Remember how to name triangles? Answer the following subsequent questions.

**Figure 4: A diagram filled with triangles**

### Example #1

In the figure above, name four obtuse triangles.

ANSWER: 1. ABD 2. AFD 3. FGD 4. ADE

### Example #2

In the figure above, name three acute triangles.

ANSWER: 1. BCD 2. FDE 3. ACE

### Example #3

What is \angleAFG?

ANSWER: A right scalene.

### Example #4

What is \angleABDF?

ANSWER: A parallelogram. (If you didn’t know this, feel free to study the page.)

### Example #5

Can you name one right triangle in the figure above? If yes, what is it?

ANSWER: \angleAFG