Free Printable Centers of Triangles Review

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.

Point O is the circumcenter of the triangle. Find OB

a)

OB = 4

b)

OB = 6

c)

OB = 5.1

d)

Not enough information

5.

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

6.

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

7.

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

8.

Which point is equidistant from the vertices?

a)

Circumcenter

b)

Incenter

c)

Neither

d)

Bilateral

9.

Which point is equidistant from the sides?

a)

Circumcenter

b)

Incenter

c)

Neither

d)

Bilateral

10.

The figure is an example of a(n) ...

a)

altitude

b)

perpendicular bisector

c)

midsegment

d)

angle bisector

11.

Find the length of PO.

a)

32

b)

35

c)

26

d)

29

12.

Given: AG = 10, find the length of BG.

a)

10

b)

20

c)

5

d)

30

13.

If m∠CAP = 34° , find ∠CAB.

a)

17°

b)

34°

c)

68°

d)

90°

14.

The orthocenter is the intersection of the ______________.

a)

Medians

b)

Perpendicular Bisectors

c)

Altitudes

d)

Angle Bisectors

15.

The centroid is the intersection of the ________________.

a)

Medians

b)

Perpendicular Bisectors

c)

Altitudes

d)

Angle Bisectors

16.

Which of the following segments represents a median?

a)

BX

b)

AZ

c)

AC

d)

BZ

17.

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

18.

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

19.

If G is the circumcenter, what type of segments are drawn?

a)

perpendicular bisectors

b)

angle bisectors

c)

altitudes

d)

centroids

20.

If Z is the centroid, what type of segments are drawn?

a)

angle bisectors

b)

perpendicular bisectors

c)

altitudes

d)

medians

21.

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

22.

[Medians and Centroid]
If AC = 16, what is AM?

a)

4

b)

8

c)

6

d)

10

23.

[Median and Centroid]
If AP = 12, what is AL?

a)

6

b)

12

c)

18

d)

24

24.

[Median and Centroid]
If NP = 5, what is CP?

a)

5

b)

8

c)

12

d)

10

25.

[Median and Centroid]
If BM = 21, what is PM?

a)

3

b)

14

c)

10

d)

7

26.

[Angle Bisectors and Incenter]:
If PX is 5, what is PZ?

a)

20

b)

10

c)

5

d)

15

27.

[Angle Bisectors and Incenter]
If PY is 6 and CY is 8, what is PC?

a)

10

b)

16

c)

24

d)

9

28.

[Angle Bisectors and Incenter]
If m<BAP is 30, what is the measure of m<PAC?

a)

60

b)

90

c)

45

d)

30

29.

[Angle Bisectors and Incenter]
If m<BCA is 72, what is m<PCA?

a)

72

b)

48

c)

60

d)

36

30.

[Perpendicular Bisectors and Circumcenter]
If AF is 6, what is AC?

a)

6

b)

10

c)

16

d)

12

31.

[Perpendicular Bisectors and Circumcenter]
If GF is 6 and GC is 11, what is FC?

a)

9.2

b)

10.5

c)

6.7

d)

8.1

32.

[Perpendicular Bisectors and Circumcenter]
If CG is 10, what is BG?

a)

5

b)

20

c)

10

d)

15

33.

[Perpendicular Bisectors and Circumcenter]
If AE is 5 and AG is 12, what is GE?

a)

9.9

b)

11

c)

10.1

d)

8

34.

The incenter is the point at which all the ____ of a triangle meet.

a)

perpendicular bisectors

b)

medians

c)

altitudes

d)

angle bisectors

35.

H is the circumcenter of triangle BCD. What is the length of GD?

a)

29

b)

26

c)

32

d)

24

36.

H is the circumcenter of triangle BCD. What is the length of BH?

a)

26

b)

32

c)

33

d)

42

37.

J is the centroid of triangle DEF. What is the length of JD?

a)

32

b)

38

c)

30

d)

36

38.

Y is the incenter of triangle STU. What is the length of VT?

a)

29

b)

26

c)

25

d)

24

39.

Y is the incenter of triangle STU. What is the length of YW?

Hint: you will have to use pythagorean theorem

a)

19

b)

12

c)

14

d)

10

40.

ED is the midsegment of triangle ABC. Find BC

a)

10.2

b)

12.5

c)

20.4

d)

22.7

41.

What is true about the midsegment EF?

a)

EF = 1/2 AB

b)

EF // AB

c)

EF = 1/2 AC

d)

none of these are true

42.

The mid segment of the triangle is 5x-1. Find the value of x.

a)

x = 6

b)

x = 7

c)

x = 11.8

d)

x = 12.4

43.

Which center of a triangle is shown in the picture below?

a)

Circumcenter

b)

Orthocenter

c)

Incenter

d)

Centroid

44.

Which center of a triangle is shown in the picture below?

a)

Circumcenter

b)

Orthocenter

c)

Incenter

d)

Centroid

45.

Which center of a triangle is shown in the picture below?

a)

Circumcenter

b)

Orthocenter

c)

Incenter

d)

Centroid

46.

Which center of a triangle is shown in the picture below?

a)

Circumcenter

b)

Orthocenter

c)

Incenter

d)

Centroid

47.

Name this center:

a)

Circumcenter

b)

Incenter

c)

Centroid

d)

Orthocenter

48.

Name this center:

a)

Circumcenter

b)

Incenter

c)

Centroid

d)

Orthocenter

49.

Name this center:

a)

Circumcenter

b)

Incenter

c)

Centroid

d)

Orthocenter

50.

Name this center:

a)

Circumcenter

b)

Incenter

c)

Centroid

d)

Orthocenter

51.

Name this center:

a)

Circumcenter

b)

Incenter

c)

Centroid

d)

Orthocenter

52.

Name this center:

a)

Circumcenter

b)

Incenter

c)

Centroid

d)

Orthocenter

53.

Name this center:

a)

Circumcenter

b)

Incenter

c)

Centroid

d)

Orthocenter

Centers of Triangles Review

Total questions: 53

Worksheet time: 2hrs 51mins

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