# Isosceles triangle

To begin to explain the **isosceles triangle** , we must also remember the definition of a triangle. We call a **polygon** a **triangle** that has three sides and is determined by three non-collinear points called **vertices** . We must also remember that the vertices are identified by means of **letters** , which are A, B and C. An isosceles triangle is a type of triangle that has at least two of its equal sides. This property is equivalent to **two angles** of the triangle that are equal. Therefore, an isosceles triangle has two equal sides and two equal angles. The name derives from the Greek **iso** (same) and **skelos** (leg).

## What is the isosceles triangle?

The isosceles triangle is a type of **polygon** that is formed by **three ****sides** , that is, it is made up of three lines which **will** be **cut** two by two and at three points that are not **aligned** .

- Characteristics of the isosceles triangle
- Properties
- Elements
- Height
- Area
- Perimeter
- How much are the angles of an isosceles triangle?
- Congruent sides
- Calculate the sides of an isosceles triangle
- How many equal angles does it have
- Examples

## Characteristics of the isosceles triangle

The main **characteristics of the isosceles triangle** are the following:

- It is made up of three
**lines**, these lines will be cut two by two. - The
**points**where the lines can be**found**are known as**vertices** - Each line
**segment**of the isosceles triangle stands as the sides of the triangle. - The two continuous sides that we find in the isosceles triangle give rise to
**the****interior****angle**. - The triangle will be made up of three
**sides**as we said, by three**vertices**, by three**interior angles**and by three**exterior angles**.

## Properties

Like other triangles, the isosceles has its properties, which are:

The **opposite angles** to the equal sides are equal. The **bisector** of the angle that is opposite the base cuts the base at its **midpoint** . The bisector always agrees with the median of side AB. The bisector of the **angle opposite** the base is **perpendicular** to the base. The bisector agrees with the corresponding height of side AB.

As isosceles triangles have a pair of equal sides, this allows them to also have certain quite recognized peculiarities both with respect to **geometry** and in their **calculations** . Every equilateral triangle is also **isosceles** , but obviously this is not necessarily **reciprocal** .

## Elements

In an isosceles triangle, there are also different elements that are part of it, among them we mention the following:

- Bisector
- Mediatrix
- Median

## Height

The height (h) of the isosceles triangle can be calculated using the Pythagorean theorem . Sides a, b / 2, and h form a right triangle . The sides b / 2 and h are the legs and to the hypotenuse .

**h ^{2} + (b / 2) ^{2} = a ^{2} → h ^{2} + (b ^{2} /4) = a ^{2} → h ^{2} = a ^{2} – (b ^{2} /4)**

Then obtaining another formula that tells us that the height of the isosceles triangle is:

**h = √ (a ^{2} – (b ^{2} /4))**

## Area

The **area of an isosceles triangle** can be calculated from the **base b (** the non-repeating side) and the **height (h)** of the **triangle** corresponding to the base. We can then say that, in this case, the area is the product of the **base** and the **height** divided by two, its formula being the following:

**Area = (b · √ (a ^{2} – (b ^{2} /4))) / 2**

## Perimeter

The **perimeter of an isosceles triangle** can be obtained by **adding** the **three sides of** the **triangle** . Having two equal sides, the perimeter is twice the repeated side (a) plus the uneven side of the geometric figure.

**Perimeter = 2 a + b**

Where a is one of the repeated sides and b the other side.

## How much are the angles of an isosceles triangle?

The isosceles right triangle has a **right angle** and **two** equal **acute ones** with a measure of **45 °** each, in this way, two sides of the triangle are equal and the other is different. The sides that are equal are known as the **legs** and the angle that is different is known as the **hypotenuse** . It is symmetrical with respect to the height of the hypotenuse, which passes through the right angle.

## Congruent sides

The **consistency** is the time one side of the triangle are congruent so that, two angles may be congruent if they have the same size and are congruent if two strokes have the same **length** . In the triangle, there can be correspondence between the **sides** and between the **angles** . Recall that the isosceles triangle is the type of triangle that has two **equal** sides and a **different** one , having two sides with the **same measure** , is considered congruent.

## Calculate the sides of an isosceles triangle

Isosceles triangles have two of their sides of equal measure and one of them has a different measure. It is also assumed that if two of the sides of an isosceles triangle are congruent or equal, this means that the opposite angles to those sides will be congruent in the same way.

## How many equal angles does it have

The isosceles triangle has two of its angles of equal measure, while the third will always be different.