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Lesson Special Lines in Triangle Public
Συνεισφορά από: Pappal
There are several different special lines for triangles
There are several different special lines for triangles
midsegment
There are several different special lines for triangles
midsegment
altitude
There are several different special lines for triangles
midsegment
altitude
median
There are several different special lines for triangles
midsegment
altitude
perpendicular bisector
median
There are several different special lines for triangles
midsegment
altitude
perpendicular bisector
median
angle bisector
There are several different special lines for triangles
Each of these has its own defintion
midsegment
altitude
perpendicular bisector
median
angle bisector
A midsegment of a triangle
A midsegment of a triangle
A
B
C
Begins at the midpoint of a side
A midsegment of a triangle
A
B
C
midpoint
Begins at the midpoint of a side
A midsegment of a triangle
A
B
C
Begins at the midpoint of a side
and goes to the midpoint
A midsegment of a triangle
of another side
A
B
C
Begins at the midpoint of a side
and goes to the midpoint
A midsegment of a triangle
of another side
A
B
C
midpoint
Begins at the midpoint of a side
and goes to the midpoint
A midsegment of a triangle
of another side
A
B
C
Begins at the midpoint of a side
and goes to the midpoint
A midsegment of a triangle
of another side
A
midsegment
B
C
If DE is a midsegment
then AD ≅ ?

EC

BE

DB

BC

A
D
B
E
C
If DE is a midsegment
EC =
A
D
B
3
E
C
The midsegment has 2 special properties
A
D
B
E
C
The midsegment has 2 special properties
it is parallel to the third side
A
D
B
E
C
The midsegment has 2 special properties
it is parallel to the third side
A
D
B
E
C
The midsegment has 2 special properties
it is parallel to the third side
A
D
B
E
C
The midsegment has 2 special properties
and half the third side
it is parallel to the third side
A
D
B
E
C
The midsegment has 2 special properties
and half the third side
it is parallel to the third side
A
D
10
B
E
C
The midsegment has 2 special properties
and half the third side
it is parallel to the third side
A
D
10
5
B
E
C
A
D
50
B
E
C
A
D
15
B
E
C
An altitude of a triangle
A
B
C
An altitude of a triangle
starts at a vertex
A
B
C
An altitude of a triangle
starts at a vertex
A
vertex
B
C
and is perpendicular
to the opposite side
An altitude of a triangle
starts at a vertex
A
B
C
and is perpendicular
to the opposite side
An altitude of a triangle
starts at a vertex
A
B
C
and is perpendicular
to the opposite side
An altitude of a triangle
starts at a vertex
A
B
C
altitude
BD is perpendicular to...

AC

BC

AB

DB

A
D
B
C
∡BDA =
∡BDC =
A
D
B
C
CE is perpendicular to...

AC

BC

AB

DB

A
E
D
B
C
All the altitudes meet at a point called the orthcenter
A
E
D
B
C
All the altitudes meet at a point called the orthcenter
A
E
D
B
C
All the altitudes meet at a point called the orthcenter
A
E
D
B
C
A median of a triangle
A
B
C
starts at the vertex
A median of a triangle
A
vertex
B
C
starts at the vertex
A median of a triangle
and goes to the midpoint
of the opposite side
A
B
C
starts at the vertex
A median of a triangle
and goes to the midpoint
of the opposite side
A
midpoint
B
C
starts at the vertex
A median of a triangle
and goes to the midpoint
of the opposite side
A
B
C
starts at the vertex
A median of a triangle
and goes to the midpoint
of the opposite side
A
B
C
median

BC

AB

AD

AC

If BD is a median
then DC ≅ ?
A
D
B
C
If BD is a median
how long is AD?
AD =
A
D
6
B
C
All the medians meet at a point called the Centroid
A
D
B
C
All the medians meet at a point called the Centroid
A
D
B
C
All the medians meet at a point called the Centroid
A
D
B
C
All the medians meet at a point called the Centroid
A
D
B
C
Altitudes meet at
Medians meet at
Orthocenter
?
Centroid
?
The centroid has 1 special property
A
D
B
C
The centroid has 1 special property
the short part of the median
A
D
B
C
The centroid has 1 special property
the short part of the median
shortpart
A
D
B
C
The centroid has 1 special property
the short part of the median
is half the long part
A
D
B
C
The centroid has 1 special property
the short part of the median
is half the long part
A
D
B
C
long
part
The centroid has 1 special property
the short part of the median
is half the long part
A
D
20
B
C
The centroid has 1 special property
the short part of the median
is half the long part
A
10
D
20
B
C
The centroid has 1 special property
the short part of the median
is half the long part
A
D
12
B
C
The centroid has 1 special property
the short part of the median
is half the long part
A
2
D
B
C
A perpendicular bisector
A
B
C
A perpendicular bisector
start at the midpoint
of a side
A
midpoint
B
C
A perpendicular bisector
and is perpendicular
start at the midpoint
to that side
of a side
A
B
C
A perpendicular bisector
and is perpendicular
start at the midpoint
to that side
of a side
A
B
C
A perpendicular bisector
and is perpendicular
start at the midpoint
to that side
of a side
A
B
perpendicular
C
bisector
DE is a perpendicular bisector
How long is AD?
AD =
A
D
E
8
B
C
DE is a perpendicular bisector
∡EDA =
A
D
E
B
C
median
?
altitude
?
perpendicular bisector
?
midsegment
?
Perpendicular bisectors meet at a point called the 
A
D
B
C
circumcenter
Perpendicular bisectors meet at a point called the 
A
D
B
C
circumcenter
Perpendicular bisectors meet at a point called the 
A
D
B
C
circumcenter
Perpendicular bisectors meet at a point called the 
A
D
B
C
circumcenter
The circumcenter is the same distance from each of the
A
D
B
C
vertices
The circumcenter is the same distance from each of the
A
D
B
C
vertices
The circumcenter is the same distance from each of the
A
D
B
C
vertices
The circumcenter is the same distance from each of the
A
D
B
C
vertices
and a circle can
The circumcenter is the same distance from each of the
be circumscribed
around the
triangle
A
D
B
C
vertices
and a circle can
The circumcenter is the same distance from each of the
be circumscribed
around the
triangle
A
D
B
C
vertices
Medians meet at
Perpendicular bisectors meet at
Altitudes meet at
centroid
?
orthocenter
?
circumcenter
?
An angle bisector
A
B
C
An angle bisector
starts at a vertex
A
B
C
An angle bisector
starts at a vertex
A
vertex
B
C
An angle bisector
starts at a vertex
and bisects the angle
A
B
C
An angle bisector
starts at a vertex
and bisects the angle
A
B
C
An angle bisector
starts at a vertex
and bisects the angle
A
B
angle bisector
C
∡ABD =
∡CBD =
∡ABC = 70
A
D
B
C
∡ABD =
∡CBD =
∡ABC = 70
A
D
B
C
∡ABD =
∡CBD = 20
∡ABC =
A
D
B
C
The angle bisectors meet at a point called the 
A
B
C
incenter
The angle bisectors meet at a point called the 
A
B
C
incenter
The angle bisectors meet at a point called the 
A
B
C
incenter
The angle bisectors meet at a point called the 
A
B
C
incenter
the incenter is equal
The angle bisectors meet at a point called the 
distance from
the sides
A
B
C
incenter
the incenter is equal
The angle bisectors meet at a point called the 
distance from
the sides
A
B
C
incenter
the incenter is equal
The angle bisectors meet at a point called the 
distance from
the sides
A
B
C
incenter
a circle can
the incenter is equal
The angle bisectors meet at a point called the 
be drawn INSIDE
distance from
the triangle
the sides
A
B
C
incenter
a circle can
the incenter is equal
The angle bisectors meet at a point called the 
be drawn INSIDE
distance from
the triangle
the sides
A
B
C
incenter
altitude
midsegment
median
perpendicular bisector
angle bisector
Fill in the missing information
midpoint
?
vertex
vertex
?
midpoint
vertex
Starts
opposite side
?
midpoint
midpoint
Ends
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