# The theorem on the median of a regular triangle

** **

In a regular triangle, the median drawn to any side is its angle bisector, height and perpendicular bisector.

Skip to content
# The median of a regular triangle. Property 1

# The theorem on the median of a regular triangle

**Proof of the theorem on the median**

**Step 1**

**Step 2**

**Step 3**

**Step 4**

# Similar topics

You are here:

- Home
- Triangles
- Chapter 7. The equilateral triangle (regular triangle)
- The median of a regular…

** **

In a regular triangle, the median drawn to any side is its angle bisector, height and perpendicular bisector.

The theorem on the median of a regular triangle

** **

Consider equilateral triangle ABC (АВ=ВС=АС).

Let BF, AD, CE be the medians.

We will prove that they are the angle bisectors, heights and perpendicular bisectors.

Proof of the theorem on the median. Step 1

** **

As АВ=АС and AD is the median to base BC, then according to the property of an isosceles triangle, AD is the height and the angle bisector.

As AD is perpendicular to side BC and divides it in half, then AD is the perpendicular bisector.

Proof of the theorem on the median. Step 2

** **

As АС=ВС and СЕ is the median to base AB, then according to the property of an isosceles triangle, CE is the height and the angle bisector.

As CE is perpendicular to side AB and divides it in half, then CE is the perpendicular bisector.

Proof of the theorem on the median. Step 3

** **

As АВ=ВС and BF is the median to base AC, then according to the property of an isosceles triangle, BF is the height and the angle bisector.

As BF is perpendicular to side AC and divides it in half, then BF is the perpendicular bisector.

The theorem is proved.

Proof of the theorem on the median. Step 4

Definition of an equilateral triangle

The criterion for a regular triangle

The area of an equilateral triangle. Formulas

The perimeter of an equilateral triangle

The angle bisector of a regular triangle. Properties

The height of a regular triangle. Properties

The property of the angles of an equilateral triangle

The exterior angle bisectors of an equilateral triangle

Similarity of regular triangle

The circle inscribed into an equilateral triangle. Properties

The circle circumscribed around a regular triangle. The theorems

Symmetry in an equilateral triangle

MATHVOX

Go to Top
This site uses cookies to help you work more comfortably. By continuing to browse the pages of the site, you agree to the use of cookies. If you need more information, please visit the Privacy Policy page. Agree

Privacy & Cookies Policy

Don`t copy text!