AnswersGeometry AIsosceles Triangles

Centroid and Orthocenter Answers

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1
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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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A
Point D can be the orthocenter because it is the point of intersection of three segments coming from the vertices of the triangle.
B
Point D can be the orthocenter because each vertex angle appears to be bisected.
C
Point D cannot be the orthocenter because the orthocenter of an obtuse triangle is located outside the triangle.
D
Point D cannot be the orthocenter because the orthocenter of an obtuse triangle is located on the perimeter of the triangle.
2
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An orthocenter is the intersection of three

A
angle bisectors in a triangle.
B
altitudes in a triangle.
C
medians in a triangle.
D
perpendicular bisectors in a triangle.
3

In which figure is point G an orthocenter?

A
Triangle A B C is a right triangle. Lines are drawn from each point to the opposite side and intersect at point G.
Option A
B
Triangle F D E is shown. Lines are drawn from each point to the opposite side and intersect at point G. The lines cut each side into 2 equal parts.
Option B
C
Triangle L M N is shown. Lines are drawn from each point to the opposite side and intersect at point G. Each angle has a different measure.
Option C
D
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.
Option D
4

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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A
Point G cannot be a centroid because JG does not equal GE.
B
Point G cannot be a centroid because JG and GE are in the ratio 1:2.
C
Point G can be a centroid because GE and JG are in the ratio 2:1.
D
Point G can be a centroid because JG + GE = JE.
5

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

Question illustration
A
11 units
B
15 units
C
43 units
D
51 units
6

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

Question illustration
A
2 inches
B
4 inches
C
8 inches
D
12 inches
7

A centroid is the intersection of three

A
altitudes in a triangle.
B
perpendicular bisectors in a triangle.
C
angle bisectors in a triangle.
D
medians in a triangle.
8

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.

Question illustration
A
5 cm
B
10 cm
C
15 cm
D
20 cm
9

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

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

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

Question illustration
A
12 units
B
17 units
C
34 units
D
51 units

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