# Isosceles triangle

🏆Practice types of triangles

## Definition of isosceles triangle

The isosceles triangle is a type of triangle that has two sides (legs) of equal length.

A consequence of having two sides of equal length implies that also the two angles opposite these sides measure the same.

## Test yourself on types of triangles!

What kid of triangle is given in the drawing?

In an isosceles triangle the two equal sides are called legs and the third is called the base and in most exercises acts as the base.

The angle that lies between the two equal sides is called the angle at the vertex (or apex angle).

The two angles adjacent to the base are called base angles and measure the same.

Furthermore, the base angles that measure the same cannot be obtuse (more than $90°$) or right angles (equal to $50°$), because their measures would add up to at least 180°, therefore, they have to be acute (less than $590°$).

The above causes the isosceles triangle to be further classified as obtuse, right or acute, depending on how the vertex angle is.

Next, we will see some examples of isosceles triangles:

### Examples of isosceles triangles

We will demonstrate the characteristics of isosceles triangles by means of an exercise.

Given the isosceles triangle $\triangle KLM$ as shown in the figure.

### Use the data shown in the illustration to calculate the angles L and M.

We will start with the triangle $\triangle KMS$. We already know two angles, so we can calculate the third angle $M$ (The sum of the interior angles of a triangle is $180°$ degrees). Thus, the angle $M$ measures $50°$ degrees (since $50° = 180° - 100° - 30°$).

Since we know that the triangle $\triangle KLM$ is isosceles we understand that its base angles $L$ and $M$ are equal.

Therefore $L=M=50°$

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## Questions on the subject

What is an isosceles triangle?

It is a triangle that has two sides of equal length.

What is an acute isosceles triangle?

It is an isosceles triangle whose angle at the vertex measures less than$90°$.

What is a right isosceles triangle?

It is an isosceles triangle whose angle at the vertex measures exactly $90°$.

If you are interested in learning more about other triangle topics, you can enter one of the following articles:

On the Tutorela blog you will find a variety of articles about mathematics.

## Ejemplos y ejercicios con soluciones de triángulo isósceles

### Exercise #1

What kid of triangle is given in the drawing?

### Step-by-Step Solution

The measure of angle C is 90°, therefore it is a right angle.

If one of the angles of the triangle is right, it is a right triangle.

Right triangle

### Exercise #2

What kind of triangle is given in the drawing?

### Step-by-Step Solution

As all the angles of a triangle are less than 90° and the sum of the angles of a triangle equals 180°:

$70+70+40=180$

The triangle is isosceles.

Isosceles triangle

### Exercise #3

What kid of triangle is the following

### Step-by-Step Solution

Given that in an obtuse triangle it is enough for one of the angles to be greater than 90°, and in the given triangle we have an angle C greater than 90°,

$C=107$

Furthermore, the sum of the angles of the given triangle is 180 degrees so it is indeed a triangle:

$107+34+39=180$

The triangle is obtuse.

Obtuse Triangle

### Exercise #4

What kind of triangle is given in the drawing?

### Step-by-Step Solution

Given that sides AB and AC are both equal to 9, which means that the legs of the triangle are equal and the base BC is equal to 5,

Therefore, the triangle is isosceles.

Isosceles triangle

### Exercise #5

Which kind of triangle is given in the drawing?

### Step-by-Step Solution

As we know that sides AB, BC, and CA are all equal to 6,

All are equal to each other and, therefore, the triangle is equilateral.