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4
3
2
1
Outside the high school program
/ Transformations
14 exercises (including 13 corrected)
a
Isometry
(14 exercices)
Isometry compound
(2 exercices)
A
B
C
D
E
F
G
H
O
A
B
C
D
E
1.
Isometry
E.2627
The
figure
b
elo
w
sho
ws
t
w
o
quadrilat-
erals
AB
C
D
and
E
F
GH
:
1
T
ak
e
the
necessary
measuremen
ts
to
complete
the
table
b
elo
w
:
AB
B
C
C
D
D
A
Mesure
(en
cm
)
E
F
F
G
GH
H
E
Mesure
(en
cm
)
2
a
Dra
w
the
straigh
t
lines
(
AE
)
,
(
B
F
)
,
(
C
G
)
and
(
D
H
)
.
What
do
y
ou
notice?
b
Name
O
the
p
oin
t
of
in
tersection
of
these
straigh
t
lines.
c
Complete
the
tables
b
elo
w
:
O
A
O
B
O
C
O
D
Mesure
(en
cm
)
O
E
O
F
O
G
O
H
Mesure
(en
cm
)
d
What
do
y
ou
notice?
E.2628
Consider
the
p
olygon
AB
C
D
E
b
elo
w
and
O
a
p
oin
t
in
the
plane.
1
a
Place
the
p
oin
t
A
on
the
half-righ
t
[
O
A
)
suc
h
that
:
O
A
=
2
·
O
A
b
Place
the
p
oin
t
B
on
the
half-righ
t
[
O
B
)
suc
h
that
:
O
B
=
2
·
O
B
c
Do
the
same
with
p
oin
ts
C
,
D
and
E
.
d
Dra
w
the
p
olygon
A
B
C
D
E
2
a
P
erform
the
follo
wing
measuremen
ts
:
AB
B
C
C
D
D
E
E
A
Mesure
(en
cm
)
A
B
B
C
C
D
D
E
E
A
Mesure
(en
cm
)
b
What
can
y
ou
sa
y
ab
out
these
t
w
o
p
olygons?
3
a
What
conjecture
can
y
ou
mak
e
ab
out
the
straigh
t
lines
(
AB
)
and
(
A
B
)
?
b
Whic
h
theorem
confirms
y
our
conjecture?
h
ttps:/
/c
hingmath.fr
chapExoCorrec/2627
sacados/2627
A
B
C
D
E
F
G
H
chapExoCorrec/2628
sacados/2628
O
A
B
C
D
E
M
N
I
J
A
B
C
D
E
O
P
I
(
d
N
M
(
d
N
M
C
C
A
B
G
E.2632
A
road
is
to
b
e
built
from
to
wn
M
to
to
wn
N
.
This
road
has
to
pass
o
v
er
a
riv
er
:
the
bridge
will
b
e
p
erp
en-
dicular
to
the
riv
erb
ed.
Place
the
bridge
(mor
e
pr
e
cisely
the
p
oints
I
and
J
)
so
that
the
length
of
the
road
is
minimal.
Hint
:
think
of
the
triangular
ine
quality.
E.2645
Consider
the
fiv
e
p
oin
ts
of
the
plane
sho
wn
b
elo
w
:
1
Determine
the
cen
ter
and
ratio
of
the
homothet
y
trans-
forming
A
in
to
C
and
B
in
to
D
.
2
Determine
the
cen
ter
of
the
homothet
y
of
ratio
3
2
trans-
forming
the
p
oin
t
B
in
to
the
p
oin
t
A
.
3
Justify
that
there
are
no
homotheties
transforming
B
in
to
C
and
D
in
to
E
.
E.2646
Consider
t
w
o
p
oin
ts
in
the
plane
O
and
P
separated
b
y
1
cm
;
the
circle
C
has
the
p
oin
t
O
as
its
cen-
ter
and
a
radius
of
3
cm
;
the
circle
C
has
cen
ter
P
and
radius
2
cm
.
Let
I
b
e
the
p
oin
t
of
in
tersection
of
the
straigh
t
line
(
O
P
)
with
the
circle
C
.
The
straigh
t
line
(
d
)
passing
through
I
in
tercepts
the
circles
C
and
C
at
M
and
N
resp
ectiv
ely
.
The
straigh
t
line
(
d
)
passing
through
I
is
secan
t
to
the
circle
C
at
M
and
also
in
tersects
the
circle
C
at
N
.
1
Sho
w
that
the
p
oin
t
I
also
b
elongs
to
the
circle
C
.
What
can
y
ou
tell
from
the
relativ
e
p
osition
of
the
t
w
o
circles
C
and
C
.
2
Determine
the
cen
ter
and
ratio
of
the
homothet
y
trans-
forming
the
circle
C
in
to
the
circle
C
.
3
Deduce
that
the
straigh
t
lines
(
N
N
)
and
(
M
M
)
are
parallel.
E.573
Let
C
b
e
a
circle
of
cen
ter
O
and
A
a
p
oin
t
of
the
circle.
Consider
the
p
oin
t
M
running
through
the
circle
C
and
I
the
middle
of
the
segmen
t
[
O
M
]
What
do
es
the
p
oin
t
I
describ
e
when
the
p
oin
t
M
describ
es
the
circle
C
?
E.574
Construct,
in
the
figure
b
elo
w,
the
p
oin
t
C
suc
h
that
AB
C
has
as
cen
ter
of
the
inscrib
ed
circle
(the
p
oin
t
of
in
tersection
of
the
bisectors)
the
p
oin
t
G
.
h
ttps:/
/c
hingmath.fr
chapExoCorrec/2632
sacados/2632
M
N
I
J
chapExoCorrec/2645
sacados/2645
A
B
C
D
E
chapExoCorrec/2646
sacados/2646
O
P
I
(
d
N
M
(
d
N
M
C
C
chapExoCorrec/573
sacados/573
chapExoCorrec/574
sacados/574
A
B
G
A
M
O
C
A
B
M
N
I
C
M
N
I
J
O
A
B
C
D
E.1839
Consider
a
circle
C
,
a
p
oin
t
A
∈
C
and
a
p
oin
t
M
that
describ
es
the
circle
:
i.e.
the
p
osition
of
M
is
v
ariable
and
it
will
tra
v
el
the
circle
C
.
Consider
the
p
oin
t
I
middle
of
[
AM
]
.
1
Place
the
p
oin
t
I
on
the
figure
ab
o
v
e.
2
a
Place
the
p
oin
t
M
diametrically
opp
osite
the
p
oin
t
A
.
Where
then
is
the
p
oin
t
I
.
b
If
the
p
oin
t
M
lies
in
A
,
where
is
the
p
oin
t
I
.
c
Place
the
p
oin
t
M
at
four
other
p
ossible
lo
cations
and
construct
the
asso
ciated
p
oin
t
I
eac
h
time
3
When
the
p
oin
t
M
describ
es
the
en
tire
circle
C
whic
h
set
describ
es
the
p
oin
t
I
.
E.1852
Consider
a
circle
C
of
diameter
[
AB
]
.
Let
M
and
N
b
e
t
w
o
p
oin
ts
of
C
distinct
from
A
and
B
.
1
Place
on
the
figure
ab
o
v
e
the
p
oin
t
J
in
tersection
of
the
straigh
t
lines
(
N
B
)
and
(
M
A
)
.
2
Sho
w
that
the
straigh
t
line
(
I
J
)
is
p
erp
endicular
to
(
B
A
)
.
E.1854
A
road
is
to
b
e
built
from
to
wn
M
to
to
wn
N
.
This
road
has
to
pass
o
v
er
a
riv
er
:
the
bridge
will
b
e
p
erp
en-
dicular
to
the
riv
erb
ed.
Place
the
bridge
(mor
e
pr
e
cisely
the
p
oints
I
and
J
)
so
that
the
length
of
the
road
is
minimal.
Hint
:
think
of
the
triangular
ine
quality.
E.1869
Consider
the
t
w
o
triangles
O
C
D
and
O
AB
rectangles
isosceles
at
O
By
means
of
a
rotation,
the
c
haracteristics
of
whic
h
will
b
e
indicated,
sho
w
that
the
segmen
ts
[
C
A
]
and
[
D
B
]
ha
v
e
the
same
length.
h
ttps:/
/c
hingmath.fr
chapExoCorrec/1839
sacados/1839
A
M
O
C
sacados/1852
A
B
M
N
I
C
chapExoCorrec/1854
sacados/1854
M
N
I
J
chapExoCorrec/1869
sacados/1869
O
A
B
C
D
A
B
C
D
E
F
A
B
C
M
M
1
M
2
M
E.1870
Consider
a
rectangle
AB
C
D
,
M
a
p
oin
t
on
[
D
C
]
,
and
N
a
p
oin
t
on
[
B
C
]
.
Determine,
in
the
figure
ab
o
v
e,
the
p
ositions
of
p
oin
ts
M
and
N
suc
h
that
the
path
passing
through
p
oin
ts
E
,
M
,
N
,
and
F
is
as
short
as
p
ossible.
(No
justific
ation
is
r
e
quir
e
d)
.
2.
Isometry
c
omp
ound
E.2631
Let
A
,
B
,
C
b
e
three
distinct
t
w
o-b
y-t
w
o
p
oin
ts
in
the
plane
and
M
b
e
an
y
p
oin
t
in
the
plane.
The
figure
opp
osite
represen
ts
the
image
M
of
M
b
y
the
transformation
S
C
O
P
Y
01
S
B
◦
S
A
where
:
S
A
(
M
)
=
M
1
;
S
B
(
M
1
)
=
M
2
;
S
C
(
M
2
)
=
M
Determine,
if
they
exist,
the
in
v
arian
ts
of
the
transformation
S
C
◦
S
B
◦
S
A
.
E.2633
Consider
in
the
plane
a
square
AB
C
D
.
Let
I
b
e
the
midp
oin
t
of
[
AB
]
.
1
Simplify
the
writing
of
the
follo
wing
transformation
:
t
−
−
→
AB
◦
t
−
→
C
A
◦
t
−
→
AC
◦
t
−
−
→
B
C
2
Establish
the
follo
wing
relationship
:
t
−
−
→
B
C
◦
S
I
◦
S
B
=
t
−
−
→
B
D
3
Determine
the
p
oin
t
M
v
erifying
the
follo
wing
relation-
ship
:
S
I
◦
S
B
=
S
M
◦
S
C
h
ttps:/
/c
hingmath.fr
chapExoCorrec/1870
sacados/1870
A
B
C
D
E
F
chapExoCorrec/2631
sacados/2631
A
B
C
M
M
1
M
2
M
chapExoCorrec/2633
sacados/2633
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