AnswersMath 3Centroid and Orthocenter

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1
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In the diagram, JG is equal to 5 cm and GE is equal to 10 cm. Based on this information, can cap g be a centroid of triangle HJK ?

A
Point cap g can be a centroid because GE and JG are in the ratio ratio of 2 to 1 .
B
Point cap g can be a centroid because JG plus GE is equal to JE .
C
Point cap g cannot be a centroid because JG and GE are in the ratio ratio of 1 to 2 .
D
Point cap g cannot be a centroid because JG does not equal GE .
2
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In triangle DEF , DG is equal to 10 cm. What is CG ?

A
15 cm
B
5 cm
C
10 cm
D
20 cm
3

What is AF ?

A
43 units
B
15 units
C
51 units
D
11 units
4

ABC is an obtuse triangle. Which is true about point cap d ?

A
Point cap d cannot be the orthocenter because the orthocenter of an obtuse triangle is located outside the triangle.
B
Point cap d can be the orthocenter because it is the point of intersection of three segments coming from the vertices of the triangle.
C
Point cap d cannot be the orthocenter because the orthocenter of an obtuse triangle is located on the perimeter of the triangle.
D
Point cap d can be the orthocenter because each vertex angle appears to be bisected.
5

A centroid is the intersection of three

A
perpendicular bisectors in a triangle.
B
medians in a triangle.
C
angle bisectors in a triangle.
D
altitudes in a triangle.
6

In which figure is point cap g an orthocenter?

A
Image with description Triangle D F E has D at the top, F at the lower left, and E at the lower right. A marked point lies on each side. The two parts of side D F have matching single tick marks, and the two parts of side D E have matching single tick marks. The two parts of side F E have matching double tick marks. Three interior segments meet at point G: one from D to the marked point on F E, one from F to the marked point on D E, and one from E to the marked point on D F.
B
Image with description Triangle A B C has A at the upper left, C at the lower left, and B at the lower right. A right-angle marker is shown at C. Three interior segments intersect at point G: one from A to side C B, one from B to side A C, and one from C to side A B.
C
Image with description Triangle L M N has L at the upper left, M at the lower left, and N at the right. Three interior segments meet at point G: one from L to side M N, one from M to side L N, and one from N to side L M. At L, matching single arc marks are shown on the two angles formed by the segment from L. At M, matching double arc marks are shown on the two angles formed by the segment from M. At N, matching triple arc marks are shown on the two angles formed by the segment from N.
D
Image with description Triangle J H K has J at the upper left, H at the lower left, and K at the right. Three interior segments meet at point G: one from J to side H K, one from H to side J K, and one from K to side J H. A right-angle marker is shown where each segment meets the opposite side.
7

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

A
an obtuse triangle
B
a right triangle
C
an acute triangle
D
an equilateral triangle
8

An orthocenter is the intersection of three

A
perpendicular bisectors in a triangle.
B
altitudes in a triangle.
C
medians in a triangle.
D
angle bisectors in a triangle.
9

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

A
obtuse.
B
isosceles.
C
acute.
D
right.
10

In triangle DFE , KJ is equal to 50 units. What is the length of segment EK ?

A
50 units
B
25 units
C
150 units
D
100 units

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