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Triangle Centers Review

Total questions: 50

Worksheet time: 4hrs 26mins

Name
Class
Date
1.
The three altitudes of a triangle intersect at the___________________.
a)
orthocenter
b)
median
c)
centroid
d)
circumcenter
2.
The altitude is __________to the side of a triangle.
a)
parallel
b)
skew
c)
off
d)
perpendicular
3.
If D is the orthocenter, what type of segments are drawn?
a)
medians
b)
altitudes
c)
angle bisectors
d)
perpendicular bisectors
4.

Name the segment/line/ray shown in the picture.

a)

Perpendicular Bisector

b)

Angle Bisector

c)

Median

d)

Altitude

5.

Name the point of concurrency shown.

a)

circumcenter

b)

incenter

c)

centroid

d)

orthocenter

6.

Which of the following points is the BALANCE POINT of a triangle. The correct method is shown in the triangle if you look at the markings.

a)

A. Circumcenter

b)

B. Orthocenter

c)

C. Centroid

d)

D. Midpoint

7.

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

8.

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

a)

6

b)

8

c)

12

d)

14

9.

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

a)

8

b)

10

c)

12

d)

16

10.

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

a)

12

b)

14

c)

17

d)

21

11.

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

a)

one third

b)

two thirds

c)

three fourths

d)

one half

12.

The centroid is the intersection point where the 3 ____ of a triangle.

a)

Medians

b)

Midsegments

c)

Perpendicular Bisectors

d)

Angle Bisectors

13.
The figure is an example of a(n) ...
a)
angle bisector
b)
midsegment
c)
altitude
d)
median
14.

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

a)

20

b)

10

c)

30

d)

15

15.

X is the centroid of the triangle. If BX = 8, find BY.

a)

4

b)

8

c)

12

d)

16

16.

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

a)

3

b)

6

c)

9

d)

12

17.

Is segment AB a median, altitude, neither or both?

a)

median

b)

altitude

c)

neither

d)

both

18.
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 
19.
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 
20.
Which point is equidistant from the vertices?
a)
Circumcenter
b)
Incenter
c)
Neither
d)
Bilateral
21.
Which point is equidistant from the sides?
a)
Circumcenter
b)
Incenter
c)
Neither
d)
Bilateral
22.
Name the point of concurrency shown.
a)
Circumcenter
b)
Incenter
c)
Supercenter
d)
Neither
23.
Name the point of concurrency shown.
a)
Circumcenter
b)
Incenter
c)
Neither
d)
Center-center
24.
Name the point of concurrency shown.
a)
Circumcenter
b)
Incenter
c)
Supercenter
d)
Neither
25.
Find the length of PO.
a)
32
b)
35
c)
26
d)
29
26.

G is the incenter. What is the length of BG?

(a)  

27.

P is the incenter of triangle JKL. Find OP.

(a)  

28.

P is the incenter. Which segment lengths are equal?

a)

KP

b)

MP

c)

PN

d)

PJ

e)

PL

29.

P is the incenter of triangle JKL. Find NP.

(a)  

30.

P is the incenter of triangle JKL. Find OP.

(a)  

31.

The figures above are examples of ...

a)

altitudes

b)

perpendicular bisectors

c)

medians

d)

angle bisectors

32.

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

a)

Circumcenter

b)

Orthocenter

c)

Incenter

d)

Centroid

33.

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

a)

Circumcenter

b)

Orthocenter

c)

Incenter

d)

Centroid

34.

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

a)

Circumcenter

b)

Orthocenter

c)

Incenter

d)

Centroid

35.

What is an angle bisector?

a)

Makes two 90 degree angles

b)

Splits a 90 degree angle in half

c)

Splits any angle into 2 congruent parts

d)

Splits a side into 2 congruent parts

36.

Based on the markings, classify each center as a circumcenter, incenter, centroid, or orthocenter.

a)

Centroid

b)

Orthocenter

c)

Circumcenter

d)

Incenter

37.

Based on the markings, classify each center as a circumcenter, incenter, centroid, or orthocenter.

a)

Centroid

b)

Orthocenter

c)

Circumcenter

d)

Incenter

38.

Based on the markings, classify each center as a circumcenter, incenter, centroid, or orthocenter.

a)

Centroid

b)

Orthocenter

c)

Circumcenter

d)

Incenter

39.

Based on the markings, classify each center as a circumcenter, incenter, centroid, or orthocenter.

a)

Centroid

b)

Orthocenter

c)

Circumcenter

d)

Incenter

40.

Based on the markings, classify each center as a circumcenter, incenter, centroid, or orthocenter.

a)

Centroid

b)

Orthocenter

c)

Circumcenter

d)

Incenter

41.

Based on the markings, classify each center as a circumcenter, incenter, centroid, or orthocenter.

a)

Centroid

b)

Orthocenter

c)

Circumcenter

d)

Incenter

42.

Based on the markings, classify each center as a circumcenter, incenter, centroid, or orthocenter.

a)

Centroid

b)

Orthocenter

c)

Circumcenter

d)

Incenter

43.

Based on the markings, classify each center as a circumcenter, incenter, centroid, or orthocenter.

a)

Centroid

b)

Orthocenter

c)

Circumcenter

d)

Incenter

44.

The three ______________ of the sides of a triangle intersect at the circumcenter.

a)

perpendicular bisectors

b)

angle bisectors

c)

medians

d)

altitudes

45.

The three ______________ of the angles of a triangle intersect at the incenter.

a)

perpendicular bisectors

b)

angle bisectors

c)

medians

d)

altitudes

46.

The three ______________ of a triangle intersect at the orthocenter.

a)

perpendicular bisectors

b)

angle bisectors

c)

medians

d)

altitudes

47.

The three ______________ of a triangle intersect at the centroid.

a)

perpendicular bisectors

b)

angle bisectors

c)

medians

d)

altitudes

48.

A(n) ______________ is equidistant from the sides of a triangle.

a)

circumcenter

b)

incenter

c)

orthocenter

d)

centroid

49.

A(n) ______________ is equidistant from the vertices of a triangle.

a)

circumcenter

b)

incenter

c)

orthocenter

d)

centroid

50.

Match the following triangle centers with the name of that center.

a)
1.

Orthocenter

b)
2.

Incenter

c)
3.

Circumcenter

d)
4.

Centroid

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