Centers of Triangles Review

1.

Multiple Choice

5 mins

1 pt

CF, BE, and AD are the medians of the triangle. If BF =10, find AF.

20

10

5

Not Enough Information

2.

Multiple Choice

3 mins

1 pt

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

4

8

12

Not Enough Information

3.

Multiple Choice

3 mins

1 pt

If G is the centroid of triangle ABC and BE= 18. Find the length of BG.

6

12

18

Not Enough Information

4.

Multiple Choice

5 mins

1 pt

If G is the centroid of triangle ABC, what is the ratio of BG to GE?

2 : 1

3 : 2

3 : 1

2 : 3

5.

Multiple Choice

3 mins

1 pt

If G is the centroid of triangle ABC and GE= 7. Find the length of BE.

7

14

21

Not Enough Informaion

6.

Multiple Choice

1 min

1 pt

The centroid is ________________ found outside a triangle.

Sometimes

Always

Never

7.

Multiple Choice

1 min

1 pt

The incenter is ________________ found inside a triangle.

Sometimes

Always

Never

8.

Multiple Choice

3 mins

1 pt

Point O is the circumcenter of the triangle. Find OB

OB = 4

OB = 6

OB = 5.1

Not enough information

9.

Multiple Choice

3 mins

1 pt

Point O is the circumcenter of the triangle. Find AC. (hint: EC is part of a right triangle)

AC = 4.45

AC = 10

AC = 8.9

Not enough information

10.

Multiple Choice

3 mins

1 pt

HK and JK are angle bisectors of the triangle. Find the measure of angle KJG

49º

50º

98º

not enough information

11.

Multiple Choice

3 mins

1 pt

HK and JK are angle bisectors of the triangle. Find the distance from K to side GJ.

50

16

21

not enough information

12.

Multiple Choice

3 mins

1 pt

Define: CIRCUMCENTER OF A TRAINGLE

the intersection point of the three perpendicular bisectors of a triangle

when a circle passes through the three vertices of a triangle

the point of intersection of three or more lines

the intersection point of the three angle bisectors of a triangle

13.

Multiple Choice

3 mins

1 pt

Define: INCENTER OF A TRIANGLE

the intersection point of the three angle bisectors of a triangle

when three or more lines intersect at a single point

the intersection point of the three perpendicular bisectors of a triangle

the point of intersection of three or more lines

14.

Multiple Choice

3 mins

1 pt

Which point is equidistant from the vertices?

Circumcenter

Incenter

Neither

Bilateral

15.

Multiple Choice

3 mins

1 pt

Which point is equidistant from the sides?

Circumcenter

Incenter

Neither

Bilateral

16.

Multiple Choice

3 mins

1 pt

Name the point of concurrency shown.

Circumcenter

Incenter

Supercenter

Neither

17.

Multiple Choice

3 mins

1 pt

Name the point of concurrency shown.

Circumcenter

Incenter

Supercenter

Neither

18.

Multiple Choice

3 mins

1 pt

Name the point of concurrency shown.

Circumcenter

Incenter

Neither

Center-center

19.

Multiple Choice

3 mins

1 pt

Name the point of concurrency shown.

Circumcenter

Incenter

neither

Pokecenter

20.

Multiple Choice

1 min

1 pt

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

angle bisector

perpendicular bisector

median

midsegment

21.

Multiple Choice

1 min

1 pt

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

altitude

perpendicular bisector

midsegment

angle bisector

22.

Multiple Choice

3 mins

1 pt

Find the length of PO.

32

35

26

29

23.

Multiple Choice

2 mins

1 pt

If m∠CAP = 34° , find ∠CAB.

17°

34°

68°

90°

24.

Multiple Choice

2 mins

1 pt

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

10

20

5

30

25.

Multiple Choice

5 mins

1 pt

1. If m<LJK = 28°, what is m<MLK?

56

112

62

124

26.

Multiple Choice

5 mins

1 pt

1. PQ is the perpendicular bisector of MN. What is QN?

7

14

10.5

28

27.

Multiple Choice

2 mins

1 pt

The orthocenter is the intersection of the ______________.

Medians

Perpendicular Bisectors

Altitudes

Angle Bisectors

28.

Multiple Choice

2 mins

1 pt

The centroid is the intersection of the ________________.

Medians

Perpendicular Bisectors

Altitudes

Angle Bisectors

29.

Multiple Choice

3 mins

1 pt

Which of the following segments represents a median?

BX

AZ

AC

BZ

30.

Multiple Choice

5 mins

1 pt

If G is the centroid of triangle ABC and BF= 10. Find the length of FA.

20

10

5

Not Enough Information

31.

Multiple Choice

5 mins

1 pt

AD = 12. Find AG

6

8

18

12

32.

Multiple Choice

5 mins

1 pt

BE = 15. Find EG.

10

5

22.5

20

33.

Multiple Choice

5 mins

1 pt

The centroid cuts each median into two segments. The shorter segment is ___________ the length of the entire segment.

one third

two thirds

three fourths

one half

34.

Multiple Choice

3 mins

1 pt

When you draw the perpendicular bisectors of a triangle it creates the point of concurrency called the _____________.

Centroid

Incenter

Circumcenter

Orthocenter

35.

Multiple Choice

3 mins

1 pt

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

perpendicular bisectors

angle bisectors

altitudes

centroids

36.

Multiple Choice

3 mins

1 pt

What is the value of x?

23

18

29

45

37.

Multiple Choice

3 mins

1 pt

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

angle bisectors

perpendicular bisectors

altitudes

medians

38.

Multiple Choice

1 min

1 pt

The orthocenter is ________________ found on the outside of a triangle.

Sometimes

Always

Never

39.

Multiple Choice

3 mins

1 pt

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

4

8

12

Not Enough Information

40.

Multiple Choice

3 mins

1 pt

If G is the centroid of triangle ABC and AG= 16. Find the length of GD.

8

16

24

Not Enough Information

41.

Multiple Choice

3 mins

1 pt

If G is the centroid of triangle ABC and BE= 18. Find the length of BG.

6

12

18

Not Enough Information

42.

Multiple Choice

3 mins

1 pt

If G is the centroid of triangle ABC and AC= 32. Find the length of CE.

16

32

48

Not Enough Information

43.

Multiple Choice

3 mins

1 pt

If G is the centroid of triangle ABC and GE= 7. Find the length of BE.

7

14

21

Not Enough Informaion

44.

Multiple Choice

1 min

1 pt

How is the orthocenter constructed?

Medians

Altitudes

Angle Bisectors

Perpendicular Bisectors

45.

Multiple Choice

1 min

1 pt

If D is the orthocenter, what type of segments are drawn?

meidans

altitudes

angle bisectors

perpendicular bisectors

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