Centroid of an Equilateral Triangle.

[Videoorchard]

Hello,

The question is taken form Geometry strategy guide. Chapter 3. Problem set. Q:6

I have understood the authors approach to this problem, and i was keen in knowing another approach( below) doesnot seem to work.

OKay so, We know that the centroid of the triangle is 360 degree. Hence
ADB=120.
CDB=120.
ADC=120.

Now, since ADB=120, and its an isosceles triangle the other two sides should sum to 60. i.e

30 (first angle) + 30 (second angle) + 120 (ADB Angle) =180 (Whole triangle)

With the above approach x=30. What am i doing wrong here?

[tommywallach]

Hey Video

While the center of the triangle adds up to 360, your mistake is in thinking that the three angles are equal (all 120). There's no reason to believe this. Remember, all we know is that those three lines are the same. Imagine you had 3 toothpicks (feel free to go grab three toothpicks). If they all meet in the center, just because they are the same length doesn't mean they are creating three equal angles. You could point two of them almost straight down and one of them straight up!

-t