Centroid and Orthocenter Answers

Triangle D E F is shown. Lines are drawn from each point to the opposite side and intersect at point G. Line segments D C, E B, and F A are formed and cut each side into 2 equal parts.

In triangle NLM, point S is the centroid, QS = (3x – 5) cm, and NS = (4x) cm.

In triangle ABC, EG = x inches and BG = (5x - 12) inches. [Figure may not be drawn to scale]

In the diagram, GB = 2x + 3..

Triangle A B C is shown. Lines are drawn from each point to the opposite side and intersect at point D.

Point G is the centroid of triangle ABC. The length of segment CG is 6 units greater than the length of segment DG.

An orthocenter is the intersection of three

In which type of triangle is the orthocenter on the perimeter of the triangle?

Point G is the centroid of triangle ABC. AG = (5x + 4) units and GF = (3x – 1) units.

If an orthocenter lies inside of a triangle, then the triangle must be