11/15/13
POW #8 - Geo 2013
Teacher: Ms. Williams
1.
4.
In which triangle do the three altitudes intersect outside the
triangle?
1. a right triangle
3. an obtuse triangle
Which of the four centers always remains on or inside a
triangle?
2. an acute triangle
4. an equilateral triangle
1. incenter, only
3. orthocenter and incenter
2. incenter and centroid
4. circumcenter, only
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2.
Point Z is the centroid of triangle ABC, E is a point on
and BE = 6. What is the length of segment
?
,
5.
Which type of triangle would have its orthocenter outside the
triangle?
1. right
3. scalene
2. obtuse
4. equilateral
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6.
Which is the point of intersection of the medians of a triangle?
1. orthocenter
3. incenter
2. centroid
4. circumcenter
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BZ =
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7.
Which point is the intersection of the altitudes of a triangle?
3.
Point Z is the centroid of triangle ABC, CA = 20, AD = 12 and
BE = 9. What is the perimeter of triangle AZE?
1. orthocenter
3. incenter
2. centroid
4. circumcenter
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8.
The incenter of a triangle can be located by finding the
intersection of the:
1.
2.
3.
4.
Perimeter of triangle AZE =
altitudes
medians
perpendicular bisectors of the three sides
angle bisectors
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11/15/13
POW #8 - Geo 2013
9.
12.
The circumcenter of a triangle can be located by finding the
intersection of the:
Given triangle ABC has vertices at (1, 3), (5, -5) and (5, -1),
respectively, find the centroid of the triangle. Round to the
nearest hundredth.
1.
2.
3.
4.
altitudes
medians
perpendicular bisectors of the three sides
angle bisectors
Centroid = (
,
)
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-------------13.
10.
Which type of triangle would have its orthocenter on the
triangle?
1. right
3. scalene
2. obtuse
4. equilateral
Given triangle ABC has vertices at (-5, 3), (1,1) and (-3,- 1),
respectively, and points E, F and G are midpoints of their
respective sides, find the centroid of the triangle. Round to the
nearest hundredth.
-------------11.
If circle O is circumscribed about triangle ABC, point O is
what point of the triangle?
1. orthocenter
3. incenter
2. circumcenter
4. centroid
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Centroid = (
,
)
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11/15/13
POW #8 - Geo 2013
14.
16.
In the diagram below, point D is the midpoint of
.
The vertices of the triangle in the diagram below are A(7,9),
B(3,3), and C(11,3).
Which of the following statements must be true?
1.
2.
3.
4.
is a median.
is an altitude.
What are the coordinates of the centroid of ΔABC?
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1. (5,6)
3. (7,5)
2. (7,3)
4. (9,6)
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15.
In the diagram below,
is perpendicular to
.
17.
In the diagram of ΔABC shown below, name the intersection of
the three lines and the type of line shown in red.
Which of the following statements must be true?
1.
2.
3.
4.
is a median.
is an altitude.
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1.
2.
3.
4.
Orthocenter, created by the altitudes
Incenter, created by the angle bisectors
Centroid, created by the medians
Circumcenter, created by the perpendicular bisectors
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11/15/13
POW #8 - Geo 2013
18.
20.
In the diagram below of ΔABC,
and
≅
.
≅
,
≅
,
As shown in the diagram below,
is a median of ΔABC.
Which statement is always true?
Point P must be the
1. centroid
3. incenter
2. circumcenter
4. orthocenter
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1.
≅
2.
≅
3. ∠ACD ≅ ∠CDB
4. ∠BCD ≅ ∠ACD
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19.
For a triangle, which two points of concurrence could be
located outside the triangle?
1.
2.
3.
4.
incenter and centroid
centroid and orthocenter
incenter and circumcenter
circumcenter and orthocenter
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