# Triangle Properties

Here are visuals for each theorem:

##### Angle Bisector Theorem:

- \(\dfrac{\overline{CA}}{\overline{CD}}=\dfrac{\overline{BA}}{\overline{DB}}\)

##### Median Theorem of a Triangle:

Concurrency and medians theorem

The distance from a vertex to the centroid is two-thirds the length of the median.

If \(\overline{AF}\), \(\overline{BE}\) and \(\overline{CD}\) are medians, then \(AG=\dfrac{2}{3} AF\), \(BG=\dfrac{2}{3}BE\) and \(CG=\dfrac{2}{3} CD\).

##### Perpendicular Bisector Theorem:

Theorem: Concurrency of Perpendicular Bisectors of a Triangle

- The perpendicular bisectors of a triangle intersect at a point that is equidistant from the vertices of a triangle.
- \(PA=PB=PC\)

##### Altitude of a Triangle:

An **altitude of a triangle** is a perpendicular segment that joins a vertex of the triangle to the opposite side.

- \(\dfrac{\text{side 1}}{\color{red}{altitude}}=\dfrac{\color{red}{altitude}}{\text{side 2}}\)