Isosceles triangle

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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.

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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° 90° ) or right angles (equal to 50° 50° ), because their measures would add up to at least 180°, therefore, they have to be acute (less than 590° 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:

Isosceles triangle

A1 isosceles triangle

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 △KLM \triangle KLM as shown in the figure.


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

A6 - Isosceles triangle

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

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

Therefore L=M=50° 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 than90° 90° .


What is a right isosceles triangle?

It is an isosceles triangle whose angle at the vertex measures exactly 90° 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 kind of triangle is given in the drawing?

404040707070707070AAABBBCCC

Video Solution

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 70+70+40=180

The triangle is isosceles.

Answer

Isosceles triangle

Exercise #2

Which kind of triangle is given in the drawing?

666666666AAABBBCCC

Video Solution

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.

Answer

Equilateral triangle

Exercise #3

What kid of triangle is the following

393939107107107343434AAABBBCCC

Video Solution

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 C=107

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

107+34+39=180 107+34+39=180

The triangle is obtuse.

Answer

Obtuse Triangle

Exercise #4

What kind of triangle is given in the drawing?

999555999AAABBBCCC

Video Solution

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.

Answer

Isosceles triangle

Exercise #5

What kind of triangle is given here?

111111555AAABBBCCC5.5

Video Solution

Step-by-Step Solution

Since none of the sides have the same length, it is a scalene triangle.

Answer

Scalene triangle

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