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4
3
2
1
Outside the middle school program
/ Midpoint theorem
4 exercises corrected
a
1.
Unclassified
financial
years
E.4793
Consider
the
parallelogram
AB
C
D
shown
below
where
AB
=
4
cm
and
I
is
the
midpoint
of
[
AB
]
.
The
point
E
is
placed
so
that
the
point
D
is
the
midpoint
of
the
segment
[
AE
]
.
The
point
J
is
the
point
of
intersection
of
the
straight
lines
(
E
I
)
and
(
C
D
)
.
The
point
F
is
the
point
of
intersection
of
the
straight
lines
(
B
C
)
and
(
E
I
)
.
1
Determine
the
measure
of
segment
[
D
J
]
.
2
a
Determine
the
value
of
the
quotient
I
B
C
J
.
b
Deduce
the
measure
of
segment
[
B
C
]
.
E.4679
In
the
plane,
consider
a
triangle
AB
C
whose
dimensions
are:
AB
=
6
cm
;
AC
=
9
cm
;
AB
C
=
60
o
Let
us
note
I
and
J
the
two
points
of
the
half-line
[
AB
)
veri-
fying
the
measures
:
AI
=
2
cm
;
AJ
=
4
cm
Note
K
and
L
the
two
points
of
the
half-line
[
AC
)
verifying
the
measures
:
AK
=
3
cm
;
AL
=
6
cm
Note
M
the
point
of
intersection
of
the
straight
lines
(
J
L
)
and
(
B
K
)
.
1
Make
a
drawing
of
this
configuration.
2
Show
that
the
straight
lines
(
I
K
)
and
(
J
L
)
are
parallel.
3
Justify
that
the
point
M
is
the
middle
of
the
segment
[
B
K
]
.
4
Show
that
the
line
(
J
L
)
is
parallel
to
the
line
(
B
C
)
.
5
Deduce
that
(
I
K
)
is
parallel
to
(
B
C
)
.
E.3672
Consider
the
figure
below
:
Data
from
the
above
figure
:
C
D
E
is
a
right
triangle
in
C
.
A
belongs
to
the
segment
[
C
D
]
,
B
belongs
to
the
segment
[
C
E
]
,
and
the
line
(
AB
)
is
parallel
to
the
line
(
D
E
)
.
The
point
F
is
the
middle
of
the
segment
[
AC
]
and
the
point
O
is
the
middle
of
[
AB
]
.
The
point
G
is
the
symmetric
of
F
with
respect
to
O
.
O
F
=
12
cm
;
AB
=
4.5
cm
;
AC
=
1.8
cm
The
following
questions
are
independent
of
each
other
:
1
What
is
the
nature
of
the
quadrilateral
AF
B
G
?
Justify.
2
Show
that
the
line
(
F
O
)
is
parallel
to
the
line
(
C
B
)
.
3
Calculate
the
length
C
D
.
4
Calculate
a
value
approximating
the
angle
to
the
nearest
degree
∠
B
AC
.
E.4792
Consider
the
parallelogram
AB
C
D
shown
below
où
:
AB
=
4
cm
;
I
is
the
middle
of
[
AB
]
.
The
point
E
is
the
symmetric
of
the
point
A
about
the
point
D
.
The
point
J
is
the
point
of
intersection
of
the
lines
(
E
I
)
and
(
C
D
)
.
The
point
F
is
the
point
of
intersection
of
the
lines
(
B
C
)
and
(
E
I
)
.
1
Determine
the
measure
of
segment
[
D
J
]
.
2
Determine
the
measure
of
segment
[
B
C
]
.
3
Determine
the
measure
of
segment
[
E
J
]
.
https://chingmath.fr
chapExoCorrec/4793
sacados/4793
A
B
C
D
E
I
J
F
3
cm
chapExoCorrec/4679
sacados/4679
Generalisation du theoreme des milieux au partage d'un segment en trois parts.
chapExoCorrec/3672
sacados/3672
C
A
B
D
E
O
F
G
chapExoCorrec/4792
sacados/4792
A
B
C
D
E
I
J
F
3
cm
4
cm
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