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Worksheets

Centroid & Orthocenter

Total questions: 28

Worksheet time: 21mins

Name
Class
Date
1.

A segment from a vertex of a triangle to the midpoint of the opposite side is called the __________.

a)

median

b)

centroid

c)

midpoint

d)

perpendicular bisector

2.

The three medians of a triangle meet at a point of concurrency called the ____________.

a)

center point

b)

midpoint

c)

centroid

d)

median point

3.
If Z is the centroid, what type of segments are drawn?
a)
angle bisectors
b)
perpendicular bisectors
c)
altitudes
d)
medians
4.
The figure is an example of a(n) ...
a)
angle bisector
b)
midsegment
c)
altitude
d)
median
5.
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
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.

The three altitudes of a triangle intersect at the?

a)

Circumcenter

b)

Incenter

c)

Centroid

d)

Orthocenter

8.

Segment AB is called _________

a)

median

b)

altitude

c)

centroid

d)

orthocenter

9.
The three altitudes of a triangle intersect at the___________________.
a)
orthocenter
b)
median
c)
centroid
d)
circumcenter
10.
The altitude is __________to the side of a triangle.
a)
parallel
b)
skew
c)

midpoint

d)
perpendicular
11.
If D is the orthocenter, what type of segments are drawn?
a)
medians
b)
altitudes
c)
angle bisectors
d)
perpendicular bisectors
12.

A segment joining a vertex to the opposite side so that is perpendiuclar to that side.

a)

perpendicular bisector

b)

angle bisector

c)

median

d)

altitude

13.
16.  For an obtuse triangle, the altitudes meet where?
a)
inside the triangle
b)
outside the triangle
c)
on the triangle
d)
the incenter
14.

Which segment is drawn?

a)

Altitude

b)

Median

c)

Angle Bisector

d)

Midsegment

15.

P is the _____.

a)

Circumcenter

b)

Incenter

c)

Centroid

d)

Orthocenter

16.

P is the _____.

a)

Circumcenter

b)

Incenter

c)

Centroid

d)

Orthocenter

17.

Which segment is the altitude to AB?

a)
FC
b)
AD
c)
EB
d)
AC
18.

If P is the centroid and BL = 12

Find BP

a)

3

b)

4

c)

8

d)

10

19.

If P is the centroid and BP = 30

Find BL

a)

10

b)

15

c)

45

d)

60

20.

If P is the centroid and CP = 18

Find PL

a)

27

b)

18

c)

12

d)

9

21.

If P is the centroid and PL = 6

Find CP

a)

12

b)

6

c)

3

d)

2

22.

If P is the centroid and AL = 42

Find PL

a)

14

b)

24

c)

28

d)

84

23.

If P is the centroid and PL = 24

Find AL

a)

8

b)

12

c)

48

d)

72

24.
CF, BE, and AD are the medians of the triangle. If BF =10, find AF.
a)
20
b)
10
c)
5
d)

15

25.

If G is the centroid of triangle ABC and AE= 4. Find the length of AC.

a)
4
b)
8
c)
12
d)

6

26.

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

a)

3

b)

6

c)

9

d)

12

27.

BD is a median of the triangle. Given DC=11, what is the length of AD?

a)

11

b)

22

c)

5.5

d)

3.67

28.

HK is an altitude in ΔGHI.

What is the value of x?

a)

42

b)

60

c)

90

d)

21