Centroid and Orthocenter

Question 1

An orthocenter is the intersection of three

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altitudes in a triangle.

Question 2

In which figure is point G an orthocenter?

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Triangle H J K is shown. Lines are drawn from each point to the opposite side to form right angles and the lines intersect at point G.

Question 3

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.

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Point G cannot be a centroid because JG and GE are in the ratio 1:2.

Question 4

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

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15 units

Question 5

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

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51 units

Question 6

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

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acute.

Question 7

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

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7 feet

Question 8

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

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34 units

Question 9

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. ?

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Show that AF is the median of BC.

Question 10

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

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9 inches

Centroid and Orthocenter Answers

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