Centroid and Orthocenter

Question 1

An orthocenter is the intersection of three

Revolt · Accepted Answer

altitudes in a triangle.

Question 2

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

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acute.

Question 3

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

Revolt · Accepted Answer

9 inches

Question 4

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

Revolt · Accepted Answer

7 feet

Question 5

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

Revolt · Accepted Answer

34 units

Question 6

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

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

Question 7

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

Revolt · Accepted Answer

a right triangle

Question 8

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. ?

Revolt · Accepted Answer

Show that AF is the median of BC.

Question 9

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

Revolt · Accepted Answer

51 units

Question 10

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

Revolt · Accepted Answer

12 inches

Centroid and Orthocenter Answers

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