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Points of Concurrency

Total questions: 24

Worksheet time: 6hrs 46mins

Name
Class
Date
1.

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

a)

Circumcenter

b)

Orthocenter

c)

Incenter

d)

Centroid

2.

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

a)

Circumcenter

b)

Orthocenter

c)

Incenter

d)

Centroid

3.

Which types of centers are ALWAYS INSIDE the triangle? (Select all that apply)

a)

Orthocenter

b)

Incenter

c)

Centroid

d)

Circumcenter

4.

What type of point of concurrency is pictured?

a)

Circumcenter

b)

Centroid

c)

Incenter

d)

Orthocenter

5.

What type of special segments are being used?

a)

Perpendicular Bisectors

b)

Angle Bisectors

c)

Medians

d)

Altitudes

6.
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 
7.

The three altitudes of a triangle intersect at the_______________.

a)

circumcenter

b)

incenter

c)

centroid

d)

orthocenter

8.

The place where all three perpendicular bisectors meet is called the ...

a)

Circumcenter

b)

Orthocenter

c)

Incenter

d)

Centroid

9.
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 
10.
Name the point of concurrency shown.
a)
Circumcenter
b)
Incenter
c)
Supercenter
d)
Neither
11.
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
12.

X is the centroid of the triangle. If AZ = 24, find AX.

a)

4

b)

8

c)

12

d)

16

13.

Point P is the circumcenter, select all segments that are equal to PB\overline{PB} .

a)

DA\overline{DA}

b)

AC\overline{AC}

c)

PC\overline{PC}

d)

PF\overline{PF}

e)

AP\overline{AP}

14.

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

a)

8

b)

16

c)

17

d)

34

15.

P is the incenter of triangle JKL. Find OP.

a)

8

b)

13

c)

17

d)

4

16.
The centroid is the point of concurrency of the 3 ____ of a triangle. 
a)
Medians
b)
Midsegments
c)
Perpendicular Bisectors
d)
Angle Bisectos
17.
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
18.
If DL = 24, then DG = 
a)
16
b)
8
c)
12
d)
36
19.
Segment AD is ________.
a)
a perpendicular segment
b)
a median 
c)
an angle bisector
d)
an altitude
20.
The figure is an example of a(n) ...
a)
altitude 
b)
perpendicular bisector
c)
median
d)
angle bisector
21.
C is the Centroid, AB = 30, AC = ?
a)
10
b)
15
c)
20
d)
5
22.
a)

9

b)

10

c)

8

d)

12

23.
a)

4

b)

1

c)

5

d)

7

24.
a)

4

b)

6

c)

12

d)

8