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Triangle Centers Test Review

Total questions: 42

Worksheet time: 2hrs 15mins

Name
Class
Date
1.
QR is a midsegment of triangle WUV. What is the length of segment QR?
a)
4
b)
8
c)
16
d)
32
2.

Fill in the blank:

A perpendicular bisector is perpendicular to and passing through the ___________________ of a segment.

a)

endpoint

b)

corner

c)

midpoint

d)

side

3.

A ray that divides an angle into two congruent angles is called .............

a)

perpendicular bisector

b)

angle bisector

c)

vertex

d)

divider

4.

Find AD

a)

8.4

b)

16.8

c)

20

d)

10

5.

Find x.

a)

54

b)

200

c)

50

d)

46

6.
TS is a midsegment of triangle GHI. Solve for the value of x.
a)
4
b)
6
c)
8
d)
10
7.
What is the measure of angle X?
a)
60
b)
40
c)
140
d)
100
8.
Name the angles from SMALLEST to LARGEST
a)
Q, R, P
b)
P, Q, R
c)
R, P, Q
d)
R, Q, P
9.
Name the sides from SMALLEST to LARGEST
a)
RS, ST, TR
b)
ST, RT, RS
c)
RT, ST, RS
d)
RT, RS, ST
10.
Can a triangle be formed with side lengths:
4, 7, 10
a)
yes
b)
no
c)
not enough information
11.
Can a triangle be formed with side lengths:
17, 9, 30
a)
yes
b)
no
c)
not enough information
12.
The longest side of a triangle would be located where on a triangle?
a)
Across from the smallest angle
b)
Across from the largest angle
c)
Cannot tell.
d)
Adjacent to the smallest side.
13.
The dotted line represents a ?...
a)
median
b)
centroid
c)
midsegment
d)
midpoint
14.
The figure is an example of a(n) ...
a)
angle bisector
b)
perpendicular bisector
c)
median
d)
midsegment
15.
The figure is an example of a(n) ...
a)
altitude 
b)
perpendicular bisector
c)
midsegment
d)
angle bisector
16.
Which of the following segments represents a median?
a)
BX
b)
AZ
c)
AC
d)
BZ
17.
The orthocenter is the intersection of the ______________.
a)
Medians
b)
Perpendicular Bisectors
c)
Altitudes
d)
Angle Bisectors
18.
The ___________________ is equidistant from the sides of the triangle.
a)
Centroid 
b)
Incenter 
c)
Orthocenter
d)
Circumcenter
19.
The centroid is the point of concurrency of the 3 ____ of a triangle. 
a)
Medians
b)
Midsegments
c)
Perpendicular Bisectors
d)
Angle Bisectos
20.
Use the Perp Bisector Theorem to find PQ
a)
10
b)
3
c)
-2
d)
5
21.
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
22.
D is the circumcenter, find ED
a)
15
b)
16
c)
17
d)
19
23.

P is the incenter of triangle JKL. Find OP.

a)

8

b)

13

c)

17

d)

4

24.
If D is the orthocenter, what type of segments are drawn?
a)
medians
b)
altitudes
c)
angle bisectors
d)
perpendicular bisectors
25.

Two sides of a triangle have the following measures.  Find the range of possible measures for the third side: 10, 9

a)

1<x<19

b)

2<x<20

c)

3<x<18

d)

2<x<19

26.

If G is the centroid of triangle ABC and GF= 4. Find the length of GC.

a)

4

b)

6

c)

8

d)

Not Enough Information

27.

In triangle ABC, BG, CE, and AF are medians that meet at D. If CG = 8, CF = 12, and AB = 25, what is the perimeter of ABC

a)

65

b)

45

c)

40

d)

35

28.

In triangle ABC, BG, CE, and AF are medians that meet at D. If AD = 2x + 6 and DF = 3x - 5, what is the value of x?

a)

4

b)

7

c)

12

d)

19

29.

Z is the circumcenter of triangle TUV. Find TU.

a)

34

b)

42

c)

30

d)

38

30.
D is the circumcenter, find EH
a)
15
b)
16
c)
17
d)
19
31.

In ΔXYZ, YB, XC, and ZA are medians.

If YC= 10, then ZC = _______

a)

15

b)

5

c)

20

d)

10

32.
In ΔXYZ, YB, XC, and ZA are medians, and YC = 15.
If XP = 8, then PC = _______
a)
2.7
b)
12
c)
5
d)
4
33.

Match the following centers of triangles.

a)
1.

Circumcenter

b)
2.

Centroid

c)
3.

Incenter

d)
4.

Orthocenter

34.

X is the centroid of the triangle. If ZX = 3, find AZ.

a)

3

b)

6

c)

9

d)

12

35.

X is the centroid of the triangle. If CW = 30, find CX.

a)

20

b)

10

c)

30

d)

15

36.

G is the incenter. Find BE. If your answer is a decimal, round to the nearest tenth.

(a)  

37.

H is the circumcenter. Find HD. If your answer is a decimal, round to the nearest tenth.

(a)  

38.

G is the incenter. Find m∠ABG. If your answer is a decimal, round to the nearest tenth.

(a)  

39.
If m∠CAP = 34° , find ∠CAB.
a)
17°
b)
34°
c)
68°
d)
90°
40.

Name this center:

a)

Circumcenter

b)

Incenter

c)

Centroid

d)

Orthocenter

41.

A circumcenter is the point at which three _____________ intersect in a triangle.

a)

Medians

b)

Altitudes

c)

Perpendicular Bisectors

d)

Angle Bisectors

42.

Find m<ZTV in the diagram above.

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