Constructions
Centoids
Review of Prerquisite
To construct a perpendicular bisector you need a ...
Fish.
Let’s begin !
A
A
Medians
B
M
C
B
M
A Median is
a segment connecting the vertex of a
triangle to the opposite midpoint.
C
A
B
A
M
C
B
M
The medians of a triangle are concurrent
at a point called the centroid.
C
A
B
M
C
Construction of the Median
Start with the FISH to find a midpoint of side BC.
Start with the base and point B.
A
B
C
Construct arc from point B past the midpoint of BC
A
B
C
Construct arc from point C past the midpoint of BC
Connect the arc intersection points to
find the midpoint.
Construct the median
A
from A to the
midpoint.
B
C
Construction of the Median from C
A
B
C
Construct arc from point B past the midpoint of BA
A
B
C
Construct arc from point A past the midpoint of BA
Connect the arc intersection points to find the
midpoint.
A
Construct
the median
from C to
B
the midpoint.
C
It is not necessary to construct all three medians because…
A
Centroid
B
Two
intersecting
lines
determine a
point.
C
It is only necessary to draw
2 medians.
The third median would only
intersect the other lines at the
same point.
We will now look at several
examples of centroids to
solidify your understanding.
A
1
A
3
C
B
C
B
2
B
4
A
A
C
B
C
Let’s try another centroid construction.
Construction of the Median
Start with the FISH to find a midpoint of side BC.
Start with the base and point B.
B
A
C
Construct arc from point B past the midpoint of BC
A
B
C
Construct arc from point C past the midpoint of BC
Connect the arc intersection points to
find the midpoint.
A
Construct the median
from A to the midpoint.
B
C
Construct arc from point B past the midpoint of BA
A
B
C
Construct arc from point A past the midpoint of BA
Connect the arc intersection points to find the
midpoint.
A
Construct
the median
from C to
the
midpoint.
B
C
It is not necessary to construct all three medians because…
Two
intersecting
lines
determine a
point.
B
A
Centroid
C
When two medians intersect
then they divide each other
into a small segment and a
large segment.
Let’s look at several situations.
A
AD = 5.26 cm
DF = 2.63 cm
E
AD
= 2.00
DF
ratio 
D
1
C
B
2
F
C
A
AD = 5.86 cm
DF = 2.93 cm
AD
= 2.00
DF
ratio 
E
D
1
C
B
2
F
C
A
AD = 6.27 cm
DF = 3.14 cm
AD
= 2.00
DF
ratio 
E
D
2
1
C
B
F
C
ratio 
2
1
A
AD = 4.06 cm
AD
= 2.00
DF = 2.03 cm
E
DF
D
C
B
F
C
The ratio is always 2:1
Therefore…
10
If DF = 5, then AD = _____
A
?
E
D
5
C
B
F
C
A
10
If DF = 5, then AD = _____
?
E
D
7
C
B
F
C
6
If AD = 12, then DF = _____
A
12
E
D
?
B
C
F
C
8
If AD = 16, then DF = _____
A
16
E
D
?
B
C
F
C
Summary
1. A Median is
a segment connecting the vertex of a
triangle to the opposite midpoint.
2. The three medians of a triangle are
concurrent.
3. The point of concurrency is called
a centroid.
Summary
4. When two medians intersect then
they divide each other into a large
segment and a small segment.
ratio 
2
1
Summary
5. The centroid is always inside the triangle.
6. To construct the median you…
You construct a fish on 2 sides.
You connect the opposite vertex
to the midpoint.
C’est fini.
Good day and good luck.
That’s all folks.
A Senior Citizen Production