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4
3
2
1
Outside the middle school program
/ angle bisector
15 exercises (100% corrected)
a
Tracing with the compass
(5 exercices)
Compass plotter program
(9 exercices)
A
x
y
30
o
A
B
C
A
x
y
B
z
t
C
r
s
A
B
C
D
1.
T
r
acing
with
the
c
omp
ass
E.1657
The
t
w
o
half-lines
[
Ax
)
and
[
Ay
)
with
origin
A
form
an
angle
of
measure
:
∠
xAy
=
30
o
Only
using
the
ruler
and
compass
:
1
Dra
w,
in
the
frame,
an
angle
∠
xAz
measuring
15
o
2
Dra
w,
within
the
frame,
an
angle
∠
xAt
measuring
60
o
E.5641
Consider
the
triangle
AB
C
sho
wn
b
e-
lo
w
:
Dra
w
the
bisectors
of
the
three
angles
of
triangle
AB
C
.
E.6446
Consider
the
three
angles
xAy
,
sB
r
and
uC
t
b
elo
w
:
Dra
w
the
bisectors
of
these
three
angles
using
a
straigh
tedge
and
compass.
E.5642
In
the
frame
b
elo
w
is
represen
ted
a
quadrilateral
AB
C
D
an
y
:
1
Dra
w
the
bisectors
of
the
four
angles
of
the
quadrilateral
AB
C
D
.
2
a
What
sp
ecial
feature
do
the
bisectors
of
this
quadri-
lateral
ha
v
e?
b
Dra
w
the
largest
p
ossible
circle
ha
ving
as
its
cen
ter
the
p
oin
t
of
in
tersection
of
the
bisectors
and
b
eing
en
tirely
con
tained
within
the
quadrilateral.
h
ttps:/
/c
hingmath.fr
chapExoCorrec/1657
sacados/1657
A
x
y
30
o
chapExoCorrec/5641
sacados/5641
A
B
C
chapExoCorrec/6446
sacados/6446
A
x
y
B
z
t
C
r
s
chapExoCorrec/5642
sacados/5642
A
B
C
D
A
B
C
D
A
B
C
D
E.5709
Consider
the
quadrilateral
AB
C
D
sho
wn
b
elo
w
:
Using
the
compass
and
a
straigh
tedge,
construct
the
four
bi-
sectors
of
the
four
angles
of
this
quadrilateral.
2.
Comp
ass
plotter
pr
o
gr
am
E.1607
1
Construct
a
triangle
AB
C
suc
h
that
:
B
AC
=
110
o
;
AB
=
6
cm
;
AC
=
10
cm
2
Construct
the
line
(
d
)
,
bisector
of
the
angle
B
AC
.
3
a
Place
the
p
oin
t
I
the
in
tersection
p
oin
t
of
the
line
(
d
)
with
the
segmen
t
[
B
C
]
.
b
Without
measuring
it,
giv
e
the
measure
of
the
angle
B
AI
4
Place
:
E
the
symmetric
of
B
with
resp
ect
to
(
d
)
F
the
symmetrical
of
C
with
resp
ect
to
(
d
)
5
What
can
b
e
said
ab
out
the
p
oin
t
of
in
tersection
of
seg-
men
ts
[
B
C
]
and
[
E
F
]
?
Justify
y
our
assertion.
E.2478
1
Dra
w
a
triangle
AB
C
v
erifying
the
follo
wing
conditions
:
AB
=
8.5
cm
;
C
AB
=
56
o
;
AB
C
=
40
o
2
Using
compass
and
ruler,
trace
the
bisector
of
the
angle
AC
B
.
3
Using
compass
and
straigh
tedge,
trace
the
bisector
of
segmen
t
[
AC
]
.
E.2543
1
Dra
w
a
triangle
AB
C
v
erifying
the
follo
wing
conditions
:
AB
=
8
cm
;
C
AB
=
62
o
;
AB
C
=
35
o
2
Using
compass
and
ruler,
a
Dra
w
the
bisector
of
the
angle
AC
B
.
b
Dra
w
the
p
erp
endicular
bisector
of
segmen
t
[
AC
]
.
E.3010
Consider
the
quadrilateral
AB
C
D
sho
wn
b
elo
w
:
1
Giv
e
the
measure
of
the
angles
AB
C
and
D
C
B
.
2
P
erform
the
follo
wing
tracing
program
using
only
the
ruler
and
compass
;
lea
v
e
y
our
tracings
presen
t
:
a
Dra
w
the
bisector
(
d
)
of
the
angle
AB
C
.
b
The
line
(
d
)
in
tercepts
the
segmen
t
[
D
C
]
at
M
.
c
Dra
w
the
p
erp
endicular
(
d
)
to
the
line
(
AB
)
passing
through
the
p
oin
t
M
.
d
Dra
w
the
p
erp
endicular
bisector
(Δ)
of
the
segmen
t
[
D
A
]
.
e
Name
N
the
p
oin
t
of
in
tersection
of
the
line
(Δ)
and
h
ttps:/
/c
hingmath.fr
chapExoCorrec/5709
sacados/5709
A
B
C
D
chapExoCorrec/1607
sacados/1607
chapExoCorrec/2478
sacados/2478
chapExoCorrec/2543
sacados/2543
chapExoCorrec/3010
sacados/3010
A
B
C
D
5
cm
5
;
5
cm
105
o
70
o
95
o
A
B
C
D
A
B
C
A
B
C
the
segmen
t
[
B
C
]
.
E.2979
Consider
the
quadrilateral
AB
C
D
sho
wn
b
elo
w
:
1
Repro
duce
this
quadrilateral
using
the
protractor.
2
Using,
only
,
the
compass
and
the
ungraduated
ruler
:
a
Dra
w
the
p
erp
endicular
bisector
of
segmen
t
[
AB
]
.
b
Dra
w
the
line
p
erp
endicular
to
the
line
(
B
C
)
passing
through
the
p
oin
t
D
.
c
Dra
w
the
bisector
of
the
angle
D
AB
.
E.4964
Consider
the
triangle
AB
C
:
1
Using
the
compass
and
ungraduated
ruler,
trace
the
three
bisectors
of
this
triangle.
2
Name
O
the
p
oin
t
of
in
tersection
of
these
three
bisectors.
3
a
Dra
w
the
circle
C
with
cen
ter
O
included
en
tirely
inside
the
triangle
AB
C
.
b
What
remarks
can
b
e
made
ab
out
the
triangle
and
the
circle
C
?
E.4963
Consider
the
triangle
AB
C
sho
wn
b
e-
lo
w
:
T
o
dra
w
the
follo
wing
lines,
use
only
the
straigh
tedge
and
the
compass
:
1
T
race
the
p
erp
endicular
bisector
of
segmen
t
[
AC
]
.
2
Dra
w
the
bisector
of
the
angle
AB
C
.
3
Dra
w
the
heigh
t
of
triangle
AB
C
from
v
ertex
C
.
E.1835
1
Dra
w
the
triangle
AB
C
ha
ving
measure
:
AB
=
5.5
cm
;
B
C
=
8
cm
;
C
A
=
4
cm
2
Dra
w
the
heigh
t
of
triangle
AB
C
originating
from
v
ertex
C
.
3
Dra
w
the
bisector
of
the
angle
AB
C
.
E.1663
1
Dra
w
a
triangle
AD
E
suc
h
that
:
AD
=
8
cm
;
AD
E
=
110
o
;
E
AD
=
30
o
2
Dra
w
the
p
erp
endicular
bisector
of
segmen
t
[
AD
]
and
call
it
(
d
)
.
3
Dra
w
the
bisector
(Δ)
of
the
angle
AE
D
using
the
pro-
tractor.
3.
Unclassifie
d
exer
cises
E.2550
1
Dra
w
the
triangle
AB
C
suc
h
that
:
AC
=
8
cm
;
AB
=
4
cm
;
B
AC
=
60
o
2
Dra
w
the
follo
wing
lines
using
ruler
and
compass
:
a
Dra
w
the
bisector
of
the
angle
B
AC
using
ruler
and
compass.
b
Name
I
the
p
oin
t
of
in
tersection
of
the
bisector
of
the
angle
B
AC
and
the
segmen
t
[
B
C
]
.
c
Dra
w
the
p
erp
endicular
bisector
of
segmen
t
[
AC
]
using
ruler
and
compass.
h
ttps:/
/c
hingmath.fr
chapExoCorrec/2979
sacados/2979
5
cm
5
;
5
cm
105
o
70
o
95
o
A
B
C
D
chapExoCorrec/4964
sacados/4964
A
B
C
chapExoCorrec/4963
sacados/4963
A
B
C
chapExoCorrec/1835
sacados/1835
La construction de ce triangle donne un angle obtus et la hauteur se trace hors du triangle.
chapExoCorrec/1663
sacados/1663
chapExoCorrec/2550
sacados/2550
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