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WorksheetsCenters of Triangles Review
Total questions: 45
Worksheet time: 2hrs 13mins
Name
Class
Date
1.
CF, BE, and AD are the medians of the triangle. If BF =10, find AF.
a)
20
b)
10
c)
5
d)
Not Enough Information
2.
If G is the centroid of triangle ABC and GF= 4. Find the length of GC.
a)
4
b)
8
c)
12
d)
Not Enough Information
3.
If G is the centroid of triangle ABC and BE= 18. Find the length of BG.
a)
6
b)
12
c)
18
d)
Not Enough Information
4.
If G is the centroid of triangle ABC, what is the ratio of BG to GE?
a)
2 : 1
b)
3 : 2
c)
3 : 1
d)
2 : 3
5.
If G is the centroid of triangle ABC and GE= 7. Find the length of BE.
a)
7
b)
14
c)
21
d)
Not Enough Informaion
6.
The centroid is ________________ found outside a triangle.
a)
Sometimes
b)
Always
c)
Never
7.
The incenter is ________________ found inside a triangle.
a)
Sometimes
b)
Always
c)
Never
8.
Point O is the circumcenter of the triangle. Find OB
a)
OB = 4
b)
OB = 6
c)
OB = 5.1
d)
Not enough information
9.
Point O is the circumcenter of the triangle. Find AC. (hint: EC is part of a right triangle)
a)
AC = 4.45
b)
AC = 10
c)
AC = 8.9
d)
Not enough information
10.
HK and JK are angle bisectors of the triangle. Find the measure of angle KJG
a)
49º
b)
50º
c)
98º
d)
not enough information
11.
HK and JK are angle bisectors of the triangle. Find the distance from K to side GJ.
a)
50
b)
16
c)
21
d)
not enough information
12.
Define: CIRCUMCENTER OF A TRAINGLE
a)
the intersection point of the three perpendicular bisectors of a triangle
b)
when a circle passes through the three vertices of a triangle
c)
the point of intersection of three or more lines
d)
the intersection point of the three angle bisectors of a triangle
13.
Define: INCENTER OF A TRIANGLE
a)
the intersection point of the three angle bisectors of a triangle
b)
when three or more lines intersect at a single point
c)
the intersection point of the three perpendicular bisectors of a triangle
d)
the point of intersection of three or more lines
14.
Which point is equidistant from the vertices?
a)
Circumcenter
b)
Incenter
c)
Neither
d)
Bilateral
15.
Which point is equidistant from the sides?
a)
Circumcenter
b)
Incenter
c)
Neither
d)
Bilateral
16.
Name the point of concurrency shown.
a)
Circumcenter
b)
Incenter
c)
Supercenter
d)
Neither
17.
Name the point of concurrency shown.
a)
Circumcenter
b)
Incenter
c)
Supercenter
d)
Neither
18.
Name the point of concurrency shown.
a)
Circumcenter
b)
Incenter
c)
Neither
d)
Center-center
19.
Name the point of concurrency shown.
a)
Circumcenter
b)
Incenter
c)
neither
d)
Pokecenter
20.
The figure is an example of a(n) ...
a)
angle bisector
b)
perpendicular bisector
c)
median
d)
midsegment
21.
The figure is an example of a(n) ...
a)
altitude
b)
perpendicular bisector
c)
midsegment
d)
angle bisector
22.
Find the length of PO.
a)
32
b)
35
c)
26
d)
29
23.
If m∠CAP = 34° , find ∠CAB.
a)
17°
b)
34°
c)
68°
d)
90°
24.
Given: AG = 10, find the length of BG.
a)
10
b)
20
c)
5
d)
30
25.
1. If m<LJK = 28°, what is m<MLK?
a)
56
b)
112
c)
62
d)
124
26.
1. PQ is the perpendicular bisector of MN. What is QN?
a)
7
b)
14
c)
10.5
d)
28
27.
The orthocenter is the intersection of the ______________.
a)
Medians
b)
Perpendicular Bisectors
c)
Altitudes
d)
Angle Bisectors
28.
The centroid is the intersection of the ________________.
a)
Medians
b)
Perpendicular Bisectors
c)
Altitudes
d)
Angle Bisectors
29.
Which of the following segments represents a median?
a)
BX
b)
AZ
c)
AC
d)
BZ
30.
If G is the centroid of triangle ABC and BF= 10. Find the length of FA.
a)
20
b)
10
c)
5
d)
Not Enough Information
31.
AD = 12. Find AG
a)
6
b)
8
c)
18
d)
12
32.
BE = 15. Find EG.
a)
10
b)
5
c)
22.5
d)
20
33.
The centroid cuts each median into two segments. The shorter segment is ___________ the length of the entire segment.
a)
one third
b)
two thirds
c)
three fourths
d)
one half
34.
When you draw the perpendicular bisectors of a triangle it creates the point of concurrency called the _____________.
a)
Centroid
b)
Incenter
c)
Circumcenter
d)
Orthocenter
35.
If G is the circumcenter, what type of segments are drawn?
a)
perpendicular bisectors
b)
angle bisectors
c)
altitudes
d)
centroids
36.
What is the value of x?
a)
23
b)
18
c)
29
d)
45
37.
If Z is the centroid, what type of segments are drawn?
a)
angle bisectors
b)
perpendicular bisectors
c)
altitudes
d)
medians
38.
The orthocenter is ________________ found on the outside of a triangle.
a)
Sometimes
b)
Always
c)
Never
39.
If G is the centroid of triangle ABC and GF= 4. Find the length of GC.
a)
4
b)
8
c)
12
d)
Not Enough Information
40.
If G is the centroid of triangle ABC and AG= 16. Find the length of GD.
a)
8
b)
16
c)
24
d)
Not Enough Information
41.
If G is the centroid of triangle ABC and BE= 18. Find the length of BG.
a)
6
b)
12
c)
18
d)
Not Enough Information
42.
If G is the centroid of triangle ABC and AC= 32. Find the length of CE.
a)
16
b)
32
c)
48
d)
Not Enough Information
43.
If G is the centroid of triangle ABC and GE= 7. Find the length of BE.
a)
7
b)
14
c)
21
d)
Not Enough Informaion
44.
How is the orthocenter constructed?
a)
Medians
b)
Altitudes
c)
Angle Bisectors
d)
Perpendicular Bisectors
45.
If D is the orthocenter, what type of segments are drawn?
a)
meidans
b)
altitudes
c)
angle bisectors
d)
perpendicular bisectors
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