Isosceles triangle

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 $90°$), because their measures would add up to at least 180°, therefore, they have to be acute (less than $90°$).

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

The Isosceles Triangle Theorem: In any isosceles triangle, the base angles are equal. Conversely, if two angles in a triangle are equal, then the triangle is isosceles.

Next, we will see some examples of isosceles triangles:

Isosceles triangle

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 $L=M=50°$

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:

• Acute triangle
• Obtuse triangle
• Scalene Triangle
• Equilateral triangle
• The edges of a triangle
• Area of a right triangle
• Height of a triangle
• How to calculate the area of a triangle
• How to calculate the perimeter of a triangle?
• Addition and difference of angles

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