# Isosceles Triangle Calculator

Explore Isosceles Triangle Online Calculator

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An isosceles triangle is a type of triangle characterized by two sides of equal length and two angles of equal measure. These two sides are known as the legs of the triangle, while the third side is called the base. The angles opposite the equal sides are also congruent, making the isosceles triangle an interesting and symmetrical geometric shape.

### Isosceles Triangle Equations Formual

Perimeter | 2 × a + b |

Area (K) | K^{2} = b^{2} * (4 × a^{2} – b^{2}) / 16 |

Angle Bisector of Side b ( t_{b} ) | t_{b}^{2} = 4 × a^{2} – b^{2} / 2 |

Media of Side a ( m_{a} ) | m_{a}^{2} = (2 * b^{2} + a^{2}) / 4 |

Angle Bisector of Side a( t_{b} ) | t_{a}^{2} = b^{2} × a × (2a + b) / (a + b)^{2} |

Media of Side b ( m_{b} ) | m_{b}^{2} = (4 * a^{2} – b^{2}) / 4 |

Inscribed Circle Radius (r) | r^{2} = b^{2} × (2a – b) / (4 × (2a + b)) |

Circumscribed Circle Radius | a / ( 2 * sin (A)) or b / ( 2 * sin (B)) |

### Properties of Isosceles Triangles

Let’s take a closer look at the properties that define isosceles triangles:

#### 1. Equal Side Lengths

As mentioned earlier, isosceles triangles have two sides of equal length. This unique feature sets them apart from other types of triangles, where all sides are typically of different lengths.

#### 2. Congruent Angles

The angles opposite the equal sides in an isosceles triangle are congruent. This means that if one of these angles measures, for example, 45 degrees, the other will also measure 45 degrees.

#### 3. Unequal Angle

The angle opposite the base of the isosceles triangle is typically different from the congruent angles. This angle is referred to as the vertex angle and is not congruent to the other two angles.

#### 4. The Base Angle Theorem

One important theorem related to isosceles triangles is the Base Angle Theorem. It states that if two sides of a triangle are congruent, then the angles opposite those sides are also congruent. This theorem is a fundamental concept in geometry and is often used in various geometric proofs.

They are real-world tools used in various disciplines. Understanding their properties and calculations can be the key to unlocking new perspectives in geometry.