Centroid and Orthocenter Answers

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

The steps shown can be used to prove that the medians of a triangle meet at a point.1. Define segments BD and CE as medians of triangle ABC.2. Write linear equations for and .3. Use a system of linear equations to solve for the coordinates of intersection point G.4. Write the equation of .5. Write an expression for the midpoint of BC, point F. 6. Show that point F lies on .7. ?

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

In triangle NQL, point S is the centroid, NS = (x + 10) feet, and SR = (x + 3) feet.

A centroid is the intersection of three

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

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

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

In triangle TRS, TZ = (3x) inches and WZ = (2x - 3) inches.[Figure may not be drawn to scale]

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

An orthocenter is the intersection of three

In triangle DEF, CG = (x + 5) units and DG = (3x - 2) units.[Figure may not be drawn to sacle]

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 which figure is point G an orthocenter?

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

Triangle H J K is shown. Lines are drawn from each point to the opposite side and intersect at point G to form line segments H C, J E, and K D.