Free Printable Centers of a Triangle

Free Printable Worksheets

Worksheets

Centers of a Triangle

Total questions: 31

Worksheet time: 18mins

Name

Class

Date

1.

The centroid is the point of concurrency of the 3 ____ of a triangle.

a)

Medians

b)

Altitudes

c)

Perpendicular Bisectors

d)

Angle Bisectos

2.

The point of concurrency of the 3 perpendicular bisectors of a triangle is called the ___?

a)

Orthocenter

b)

Incenter

c)

Circumcenter

d)

Centriod

3.

Which point of concurrency is the intersection of the angle bisectors of a triangle?

a)

centroid

b)

incenter

c)

orthocenter

d)

circumcenter

4.

Which of the following statements is correct about the circumcenter of a triangle?

a)

It's the intersection of the bisectors of the triangle's three angles AND

is equidistant from the triangle's three vertices

b)

It's the intersection of the bisectors of the triangle's three angles AND

is equidistant from the triangle's three sides

c)

It's the intersection of the perpendicular bisectors of the triangle's three sides AND

is equidistant from the triangle's three vertices

d)

It's the intersection of the altitudes of the triangle's three sides AND

is equidistant from the triangle's three vertices

5.

Which of the following statements is correct about the incenter of a triangle?

a)

It's the intersection of the bisectors of the triangle's three angles AND

is equidistant from the triangle's three vertices

b)

It's the intersection of the bisectors of the triangle's three angles AND

is equidistant from the triangle's three sides

c)

It's the intersection of the perpendicular bisectors of the triangle's three sides AND

is equidistant from the triangle's three vertices

d)

It's the intersection of the altitudes of the triangle's three sides AND

is equidistant from the triangle's three vertices

6.

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

7.

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

a)

angle bisectors

b)

perpendicular bisectors

c)

altitudes

d)

medians

8.

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

a)

angle bisector

b)

perpendicular bisector

c)

median

d)

altitude

9.

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

a)

angle bisector

b)

perpendicular bisector

c)

altitude

d)

median

10.

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

a)

altitude

b)

perpendicular bisector

c)

median

d)

angle bisector

11.

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

12.

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

a)

7

b)

14

c)

21

d)

Not Enough Informaion

13.

Point O is the circumcenter of the triangle. Find OB

a)

OB = 4

b)

OB = 6

c)

OB = 5.1

d)

Not enough information

14.

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

a)

20

b)

10

c)

5

d)

15

15.

Point G is the circumcenter.

If AF is 6, what is AC?

a)

6

b)

10

c)

16

d)

12

16.

If m∠CAP = 34° , find ∠CAB.

a)

A. 17°

b)

B. 34°

c)

C. 68°

d)

D. 90°

17.

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

18.

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

19.

Which point is equidistant from the vertices?

a)

Circumcenter

b)

Incenter

c)

Neither

d)

Bilateral

20.

Which point is equidistant from the sides?

a)

Circumcenter

b)

Incenter

c)

Neither

d)

Bilateral

21.

Name the point of concurrency shown.

a)

Circumcenter

b)

Incenter

c)

Supercenter

d)

Neither

22.

Name the point of concurrency shown.

a)

Circumcenter

b)

Incenter

c)

Centroid

d)

Orthocenter

23.

The altitudes of a triangle intersect at the _________________________.

a)

Centriod

b)

Circumcenter

c)

Incenter

d)

Orthocenter

24.

What is an angle bisector?

a)

Makes two 90 degree angles

b)

splits a 90 degree angle in half

c)

splits any angle in half

d)

splits 2 sides in half

25.

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

a)

perpendicular bisectors

b)

angle bisectors

c)

altitudes

d)

centroids

26.

Which of the following segments represents an altitude?

a)

BX

b)

AZ

c)

AC

d)

BZ

27.

Which of the following segments represents a median?

a)

BX

b)

AZ

c)

AC

d)

BZ

28.

Which of the following words describes the point shown in the figure?

a)

Centerpoint

b)

Orthocenter

c)

Centroid

d)

Altitude-point

29.

If S is the incenter, what type of segments are drawn?

a)

medians

b)

angle bisectors

c)

perpendicular bisectors

d)

altitudes

30.

Which point of concurrency is this?

a)

Circumcenter

b)

Orthocenter

c)

Incenter

d)

Centroid

31.

The circumcenter is _________________ in the triangle.

a)

always

b)

sometimes

c)

never

d)

definitely

100 %

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