GEOM 2 | Lesson 4 | Watch (Triangle Properties)

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.

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


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