Centroid and Orthocenter

In triangle ABC, EG = x inches and BG = (5x - 12) inches What is EB?

12 inches

In triangle DEF, CG = (x + 5) units and DG = (3x - 2). What is DG?

34 units

In triangle DEF, DG = 10 cm. What is CG?

5cm

In triangle TRS, TZ = (3x) inches and WZ = (2x - 3) inches. What is WZ?

9 inches

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

A. a right triangle

An orthocenter is the intersection of three

B. altitudes in a triangle

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

C. 18 units

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

C. 20 cm

ABC is an obtuse triangle. Which is true about point D?

C. Point D cannot be the orthocenter because the orthocenter of an obtuse triangle is located outside the triangle.

In which figure is point G an orthocenter?

D.

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

D. 51 units

A centroid is the intersection of three

D. medians in a triangle.