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Grade 6
/ Axial symmetry
43 exercises (100% corrected)
a
Introduction
(3 exercices)
Symmetry and grids
(7 exercices)
Symmetry and frieze
(2 exercices)
Traced on white paper
(7 exercices)
Drawing on white paper and circle
(3 exercices)
Figures with axis of symmetry
(3 exercices)
Axes of symmetry and median
(2 exercices)
Search for the axis of symmetry
(4 exercices)
Figure without axis of symmetry
(2 exercices)
Introduction to the properties of symmetry
(4 exercices)
Properties of symmetry
(4 exercices)
Axes of symmetry and bisector
(1 exercice)
Construction program and axis of symmetry
(1 exercice)
Angle Bisector
(1 exercice)
image PNG : /home/_math/_exercice/d1/1617/metapost/01.png
1.
Intr
o
duction
E.6662
F
or
eac
h
of
the
figures,
is
it
p
ossible
to
find
a
folding
axis
so
that
the
figure
is
p
erfectly
sup
erim-
p
osed
on
itself?
If
so,
sho
w
the
folding
axis(es)
on
the
figures.
E.1617
Belo
w
is
giv
en
the
represen
tation
of
a
butterfly
where
8
dots
ha
v
e
b
een
mistak
en
in
evidence.
1
F
old
the
leaf
of
sort
as
if
the
butterfly
folds
the
wing.
Note
that
the
dots
put
in
evidence
are
o
v
erlapping
p
er-
fectly
.
2
a
Relating
b
y
one
segmen
t
eac
h
couple
of
p
oin
ts
ˇ
twins
ı.
b
What
can
w
e
sa
y
ab
out
the
p
osition
of
these
segmen
ts
b
et
w
een
them?
c
What
can
dire
of
these
segmen
ts
relativ
ely
to
the
axisof
folding?
h
ttps:/
/c
hingmath.fr
chapExoCorrec/6662
sacados/6662
chapExoCorrec/1617
sacados/1617
(
d
A
B
C
D
A
B
C
D
E
(
d
A
B
C
D
(
d
(
d
E.11814
The
figure
b
elo
w
sho
ws
a
straigh
t
line
(
d
)
and
four
p
oin
ts
in
the
plane
:
1
P
erform
the
follo
wing
plot
program
:
a
Dra
w
the
line
(
d
1
)
p
erp
endicular
to
the
line
(
d
)
passing
through
the
p
oin
t
A
.
b
Name
H
the
p
oin
t
of
in
tersection
of
(
d
1
)
with
the
line
(
d
)
.
c
Place
the
p
oin
t
A
,
distinct
from
A
,
on
the
line
(
d
1
)
v
erifying
distance
equalit
y
:
AH
=
H
A
2
P
erform
the
follo
wing
plot
program
:
a
Dra
w
the
line
(
d
2
)
p
erp
endicular
to
the
line
(
d
)
passing
through
the
p
oin
t
B
.
b
Name
I
the
p
oin
t
of
in
tersection
of
(
d
2
)
and
(
d
)
.
c
Place
the
p
oin
t
B
,
distinct
from
B
,
on
the
straigh
t
line
(
d
2
)
suc
h
that
w
e
ha
v
e
the
follo
wing
equalit
y
of
distance
:
B
I
=
I
B
3
Carry
out
the
same
t
yp
e
of
plot
for
p
oin
ts
C
and
D
.
4
a
Dra
w
the
quadrilateral
AB
C
D
.
What
is
its
nature?
b
Dra
w
the
quadrilateral
A
B
C
D
.
What
is
its
nature?
c
What
can
w
e
sa
y
ab
out
these
t
w
o
quadrilaterals
rela-
tiv
e
to
the
line
(
d
)
?
2.
Symmetry
and
grids
E.1621
Dra
w
the
symmetric
of
the
p
olygon
AB
C
D
E
with
resp
ect
to
the
axis
(
d
)
:
E.3060
Dra
w
the
symmetry
of
the
quadri-
lateral
AB
C
D
with
resp
ect
to
the
axis
(
d
)
:
E.9999
Create
the
image
of
the
p
olygon
b
elo
w
b
y
reflecting
it
across
the
axis
(
d
)
:
h
ttps:/
/c
hingmath.fr
chapExoCorrec/11814
sacados/11814
(
d
A
B
C
D
chapExoCorrec/1621
sacados/1621
A
B
C
D
E
(
d
chapExoCorrec/3060
sacados/3060
A
B
C
D
(
d
chapExoCorrec/9999
sacados/9999
(
d
A
B
C
D
E
(
d
A
B
C
D
(
d
(
d
A
B
C
(
d
(
d
E.3061
Dra
w
the
symmetric
of
the
p
olygon
AB
C
D
E
with
resp
ect
to
the
axis
(
d
)
:
E.2683
P
erform
the
image
of
the
p
olygon
b
elo
w
b
y
symmetry
ab
out
the
axis
(Δ)
.
E.6680
Dra
w
the
symmetric
of
the
p
olygon
AB
C
D
E
with
resp
ect
to
the
axis
(
d
)
:
E.3086
The
figure
b
elo
w
is
made
up
of
a
triangle
and
a
half-disc.
1
Dra
w
the
symmetrical
of
this
figure
with
resp
ect
to
the
(
d
)
axis.
2
Dra
w
the
symmetrical
of
this
figure
with
resp
ect
to
the
(Δ)
axis.
3.
Symmetry
and
frieze
E.7892
A
gra
y
p
olygon
is
sho
wn
b
elo
w
:
Construct
the
symmetric
of
this
p
olygon
relativ
e
to
the
line
(
d
)
.
E.7893
Consider
the
shaded
p
olygon
sho
wn
b
elo
w
:
Dra
w
the
symmetrical
line
of
the
p
olygon
with
resp
ect
to
the
(
d
)
axis.
h
ttps:/
/c
hingmath.fr
chapExoCorrec/3061
sacados/3061
A
B
C
D
E
(
d
chapExoCorrec/2683
sacados/2683
chapExoCorrec/6680
sacados/6680
A
B
C
D
(
d
chapExoCorrec/3086
sacados/3086
(
d
A
B
C
chapExoCorrec/7892
sacados/7892
(
d
chapExoCorrec/7893
sacados/7893
(
d
A
B
C
(
d
A
B
C
(
d
A
B
C
D
(
d
(
d
4.
T
r
ac
e
d
on
white
p
ap
er
E.2640
Dra
w
the
symmetric
of
the
triangle
AB
C
relativ
e
to
the
line
(
d
)
.
E.2642
In
the
frame
b
elo
w,
consider
the
triangle
AB
C
and
the
straigh
t
line
(
d
)
.
1
Place
the
follo
wing
p
oin
ts
in
the
frame
ab
o
v
e
:
a
The
p
oin
t
A
symmetrical
to
the
p
oin
t
A
relativ
e
to
the
line
(
d
)
.
b
The
p
oin
t
B
symmetrical
to
the
p
oin
t
B
relativ
e
to
the
line
(
d
)
.
c
The
p
oin
t
C
suc
h
that
C
and
C
are
symmetrical
rel-
ativ
e
to
the
line
(
d
)
.
2
Dra
w
the
triangle
A
B
C
.
E.2641
Dra
w
the
symmetric
of
the
rectangle
AB
C
D
relativ
e
to
the
line
(
d
)
.
E.1609
Consider
a
quadrilateral
Q
and
a
straigh
t
line
(
d
)
passing
through
t
w
o
v
ertices
opp
osite
this
quadrilateral.
Dra
w
the
symmetric
of
the
quadrilateral
Q
with
resp
ect
to
the
axis
(
d
)
h
ttps:/
/c
hingmath.fr
chapExoCorrec/2640
sacados/2640
A
B
C
(
d
chapExoCorrec/2642
sacados/2642
A
B
C
(
d
chapExoCorrec/2641
sacados/2641
A
B
C
D
(
d
chapExoCorrec/1609
sacados/1609
(
d
(
d
(
d
A
B
C
E.1612
Consider
the
quadrilateral
and
the
line
(
d
)
sho
wn
b
elo
w
:
Dra
w
the
symmetric
of
the
quadrilateral
with
resp
ect
to
the
(
d
)
axis.
E.2684
Consider
b
elo
w
a
quadrilateral
and
the
line
(
d
)
.
Dra
w
the
symmetric
of
the
quadrilateral
with
resp
ect
to
the
line
(
d
)
.
E.3062
Consider
the
triangle
AB
C
sho
wn
in
the
frame
b
elo
w
:
1
a
Dra
w
the
symmetrical
A
of
the
p
oin
t
A
with
resp
ect
to
the
line
(
B
C
)
.
b
Dra
w
the
symmetrical
B
of
the
p
oin
t
B
with
resp
ect
to
the
line
(
AC
)
.
c
Dra
w
the
symmetrical
C
of
the
p
oin
t
C
with
resp
ect
to
the
line
(
AB
)
.
2
Dra
w
the
triangle
A
B
C
.
5.
Dr
awing
on
white
p
ap
er
and
cir
cle
E.10016
Consider
the
line
(Δ)
and
the
fig-
ure
comp
osed
of
a
triangle
and
a
semicircle,
one
diameter
of
whic
h
is
a
side
of
the
triangle.
Dra
w
the
symmetric
of
the
figure
ab
out
the
(Δ)
axis.
h
ttps:/
/c
hingmath.fr
chapExoCorrec/1612
sacados/1612
(
d
chapExoCorrec/2684
sacados/2684
(
d
chapExoCorrec/3062
sacados/3062
A
B
C
chapExoCorrec/10016
sacados/10016
(
d
a
b
c
d
e
f
g
h
i
j
k
l
La
symétrie
axiale
a`c
he
les
mots
a
v
ec
un
e∑et
miroir
La
symétrie
axiale
a`c
he
les
mots
a
v
ec
un
e∑et
miroir
E.10017
Consider
b
elo
w
the
straigh
t
line
(
d
)
and
a
figure
comp
osed
of
a
triangle
and
a
semicircle,
one
of
whose
diameters
is
a
side
of
the
triangle
Dra
w
the
symmetric
of
the
figure
ab
out
the
(
d
)
axis.
E.10015
Sho
wn
b
elo
w
is
a
straigh
t
line
(Δ)
and
a
figure
F
consisting
of
a
rectangle
and
a
semicircle
whose
diameter
is
one
of
the
rectangle’s
sides
Dra
w
the
symmetric
of
F
with
resp
ect
to
(Δ)
.
6.
Figur
es
with
axis
of
symmetry
E.6410
Whic
h
of
the
follo
wing
signs
ha
v
e
one
or
more
axes
of
symmetry
:
F
or
eac
h
sign,
giv
e
the
n
um
b
er
of
axes
of
symmetry
that
it
admits.
E.3059
Consider
the
figure
comp
osed
of
the
t
w
o
texts
b
elo
w.
This
figure
has
an
axis
of
symmetry
.
Sho
w
this
axis.
h
ttps:/
/c
hingmath.fr
chapExoCorrec/10017
sacados/10017
(
d
chapExoCorrec/10015
sacados/10015
chapExoCorrec/6410
sacados/6410
a
b
c
d
e
f
g
h
i
j
k
l
chapExoCorrec/3059
sacados/3059
La
symétrie
axiale
a`c
he
les
mots
a
v
ec
un
e∑et
miroir
La
symétrie
axiale
a`c
he
les
mots
a
v
ec
un
e∑et
miroir
a
b
c
d
(
d
A
B
A
B
E.11063
F
our
sp
ecial
quadrilaterals
are
sho
wn
b
elo
w
:
F
or
eac
h
of
them
:
Giv
e
the
nature
of
the
quadrilateral
;
Dra
w,
freehand,
the
axes
of
symmetry
in
the
figure
;
Giv
e
the
n
um
b
er
of
axes
of
symmetry
in
the
figure.
7.
Axes
of
symmetry
and
me
dian
E.5574
Consider
the
configuration
b
elo
w
:
1
W
e’ll
lea
v
e
the
construction
lines
when
w
e
complete
the
figure
:
a
Construct
the
p
oin
t
A
symmetrical
to
the
p
oin
t
A
relativ
e
to
the
line
(
d
)
.
b
Construct
the
p
oin
t
B
symmetrical
to
the
p
oin
t
B
relativ
e
to
the
line
(
d
)
.
2
What
is
the
nature
of
the
quadrilateral
AA
B
B
?
Justify
y
our
answ
er.
3
What
do
es
the
line
(
d
)
represen
t
for
the
segmen
t
[
AA
]
?
E.1620
1
a
Dra
w
the
circle
with
cen
ter
A
and
radius
5
cm
.
Dra
w
the
circle
with
cen
ter
B
and
radius
5
cm
.
b
Name
M
and
N
the
p
oin
ts
of
in
tersection
of
these
t
w
o
circles.
Dra
w
the
straigh
t
line
(
M
N
)
.
2
Giv
e
all
the
geometric
prop
erties
of
the
figure.
Pro
vide
the
necessary
co
ding
for
y
our
figure.
3
a
What
is
the
symmetric
of
p
oin
t
A
relativ
e
to
axis
(
M
N
)
?
b
What
is
the
symmetric
of
the
p
oin
t
B
relativ
e
to
the
axis
(
M
N
)
?
c
Relativ
e
to
the
[
AB
]
segmen
t,
what
can
b
e
said
ab
out
the
(
M
N
)
axis?
4
Dra
w
the
t
w
o
circles
of
radius
4
cm
ha
ving
the
p
oin
ts
A
and
B
as
their
resp
ectiv
e
cen
ters.
What
do
w
e
notice?
8.
Se
ar
ch
for
the
axis
of
symmetry
h
ttps:/
/c
hingmath.fr
chapExoCorrec/11063
sacados/11063
a
b
c
d
chapExoCorrec/5574
sacados/5574
(
d
A
B
chapExoCorrec/1620
sacados/1620
A
B
A
B
C
E
F
G
A
B
C
D
E
F
G
H
A
B
D
E
C
A
B
D
E
C
E.10877
Reminder
:
The
median
of
a
segmen
t
[
AB
]
is
the
unique
line
(
d
)
that
satisfies
the
follo
wing
t
w
o
prop
erties
:
The
line
(
d
)
passes
through
the
midp
oin
t
of
the
segmen
t
[
AB
]
.
The
line
(
d
)
is
p
erp
endicular
to
the
line
(
AB
)
.
Consider
the
figure
b
elo
w
represen
ting
t
w
o
triangles
:
1
Dra
w
the
p
erp
endicular
bisector
(
d
)
of
the
segmen
t
[
AE
]
using
a
ruler
and
a
set
square.
2
Chec
k
that
the
line
(
d
)
is
also
the
p
erp
endicular
bisector
of
the
segmen
t
[
B
F
]
.
3
What
else
needs
to
b
e
c
hec
k
ed
to
confirm
that
triangle
E
F
G
is
the
image
of
triangle
AB
C
under
the
symmetry
axis
(
d
)
?
E.1611
The
figure
b
elo
w
sho
ws
t
w
o
quadri-
laterals
:
1
Assuming
that
this
figure
admits
an
axis
of
symmetry
,
sp
ecify
the
p
ossible
image
of
the
p
oin
t
A
;
of
the
p
oin
t
B
.
2
a
Dra
w,
with
compass
and
unlined
straigh
tedge,
the
p
erp
endicular
bisector
(
d
)
of
the
segmen
t
[
AF
]
.
b
What
do
es
the
line
(
d
)
represen
t
for
the
segmen
t
[
B
E
]
?
Can
w
e
sa
y
that
the
p
oin
t
B
admits
the
p
oin
t
E
as
symmetrical
with
resp
ect
to
the
line
(
d
)
?
c
Chec
k
that
the
p
oin
ts
D
and
G
are
symmetrical
with
resp
ect
to
the
line
(
d
)
.
3
What
remains
to
b
e
c
hec
k
ed
to
confirm
that
the
line
(
d
)
is
an
axis
of
symmetry
of
this
figure?
E.2657
The
figure
b
elo
w
sho
ws
t
w
o
p
oly-
gons
:
1
a
Dra
w
the
straigh
t
line
(
d
)
p
erp
endicular
bisector
of
the
segmen
t
[
AA
]
using
compass
and
straigh
tedge.
b
What
is
the
axis
of
symmetry
transforming
p
oin
t
A
in
to
A
?
2
a
Dra
w
the
straigh
t
line
(
d
)
p
erp
endicular
bisector
of
the
segmen
t
[
B
B
]
using
compass
and
straigh
tedge.
b
What
is
the
axis
of
symmetry
transforming
p
oin
t
B
in
to
B
?
3
Do
es
this
figure
admit
an
axis
of
symmetry?
E.3085
Consider
the
figure
b
elo
w,
whic
h
has
t
w
o
axes
of
symmetry
.
Construct
its
t
w
o
axes
of
symmetry
.
h
ttps:/
/c
hingmath.fr
chapExoCorrec/10877
sacados/10877
A
B
C
E
F
G
chapExoCorrec/1611
sacados/1611
A
B
C
D
E
F
G
H
chapExoCorrec/2657
sacados/2657
A
B
D
E
C
A
B
D
E
C
chapExoCorrec/3085
sacados/3085
A
B
C
D
E
F
A
B
C
D
E
F
G
H
(
d
A
B
C
D
A
B
C
9.
Figur
e
without
axis
of
symmetry
E.11026
Consider
the
t
w
o
triangles
AB
C
and
D
E
F
sho
wn
b
elo
w
:
1
a
Dra
w
the
bisector
of
the
segmen
t
[
B
E
]
.
b
Dra
w
the
p
erp
endicular
bisector
of
segmen
t
[
AD
]
.
2
Are
the
t
w
o
triangles
AB
C
and
D
E
F
symmetrical?
E.2685
Consider
the
figure
sho
wn
b
elo
w
comp
osed
of
t
w
o
quadrilaterals.
Sho
w
that
this
figure
do
es
not
ha
v
e
an
axis
of
symmetry
.
Jus-
tify
y
our
approac
h.
10.
Intr
o
duction
to
the
pr
op
erties
of
symmetry
E.1619
1
Dra
w
the
quadrilateral
A
B
C
D
symmetrical
to
the
quadrilateral
AB
C
D
b
y
axial
symmetry
of
axis
(
d
)
.
2
a
Using
the
compass,
compare
distances
:
AD
and
A
D
;
AC
and
A
C
b
Using
the
square,
compare
the
angles
B
C
D
and
B
C
D
?
3
Whic
h
prop
erties
seem
to
preserv
e
axial
symmetry?
E.3054
Consider
in
the
frame
b
elo
w
the
triangle
AB
C
and
the
straigh
t
line
(Δ)
:
1
Dra
w
the
symmetric
of
the
AB
C
triangle
with
resp
ect
to
the
(Δ)
axis.
2
a
Compare
the
measure
of
segmen
ts
[
AB
]
,
[
AC
]
,
[
B
C
]
resp
ectiv
ely
with
their
symmetries.
b
Using
the
protractor,
compare
the
measure
of
the
an-
gles
AB
C
,
AC
B
,
B
AC
resp
ectiv
ely
with
their
symme-
tries.
h
ttps:/
/c
hingmath.fr
chapExoCorrec/11026
sacados/11026
A
B
C
D
E
F
chapExoCorrec/2685
sacados/2685
A
B
C
D
E
F
G
H
chapExoCorrec/1619
sacados/1619
(
d
A
B
C
D
chapExoCorrec/3054
sacados/3054
A
B
C
A
B
(
d
(
d
A
B
A
B
C
(
d
E.1606
Consider
b
elo
w
a
straigh
t
line
(
d
)
and
t
w
o
p
oin
ts
A
and
B
of
the
plane
:
1
Construct
the
p
oin
ts
A
and
B
resp
ectiv
ely
symmetrical
to
A
and
B
with
resp
ect
to
the
line
(
d
)
.
2
Dra
w
the
straigh
t
lines
(
AB
)
and
(
A
B
)
.
What
can
b
e
said
ab
out
the
p
oin
t
of
in
tersection
of
the
lines
(
AB
)
and
(
A
B
)
?
Justify
y
our
answ
er.
E.1610
1
a
In
the
plane,
dra
w
a
straigh
t
line
(
d
)
and
t
w
o
p
oin
ts
A
and
B
on
either
side
of
(
d
)
.
b
Dra
w
the
segmen
t
[
AB
]
and
name
O
the
p
oin
t
of
in-
tersection
of
the
segmen
t
[
AB
]
and
the
line
(
d
)
.
c
Construct
the
symmetrical
p
oin
ts
of
A
and
B
with
re-
sp
ect
to
(
d
)
.
Name
them
A
and
B
,
resp
ectiv
ely
.
2
What
remarks
can
b
e
made
ab
out
this
figure?
Justify
y
our
answ
ers.
11.
Pr
op
erties
of
symmetry
E.1613
T
racings
m
ust
b
e
made
on
white
pap
er
:
1
Dra
w
a
straigh
t
line
(
d
)
and
place
a
p
oin
t
M
in
the
plane
not
b
elonging
to
the
straigh
t
line
(
d
)
.
2
a
Dra
w
the
p
oin
t
N
symmetrical
to
the
p
oin
t
M
with
resp
ect
to
the
line
(
d
)
.
b
What
do
es
the
line
(
d
)
represen
t
for
the
segmen
t
[
M
N
]
?
3
a
Place
a
p
oin
t
P
v
erifying
the
follo
wing
t
w
o
condi-
tions
:
P
∈
(
d
)
;
P
∈
[
M
N
]
b
Dra
w
the
triangle
M
N
P
.
c
What
is
the
nature
of
the
triangle
M
N
P
?
Justify
y
our
answ
er.
E.1614
1
Dra
w
the
rectangle
AB
C
D
suc
h
that
:
AB
=
8
cm
;
AC
=
9
cm
2
Name
O
the
p
oin
t
of
in
tersection
of
the
diagonals.
Dra
w
the
circle
C
with
cen
ter
O
passing
through
the
p
oin
t
B
.
What
do
w
e
notice?
Justify
y
our
answ
er
3
Dra
w
the
symmetric
of
the
p
oin
t
A
with
resp
ect
to
the
line
(
B
D
)
.
What
do
w
e
notice?
Justify
y
our
answ
er.
E.1608
Dra
w
a
circle
with
cen
ter
I
,
then
t
w
o
straigh
t
lines
(Δ)
and
(
d
)
passing
through
I
.
By
a
single
strok
e
of
the
compass
and
a
single
strok
e
of
the
ruler
,
dra
w
the
symmetrical
of
the
straigh
t
line
(
d
)
with
resp
ect
to
the
straigh
t
line
(Δ)
E.5577
Consider
the
figure
b
elo
w,
where
triangle
AB
C
extends
b
ey
ond
the
frame
sho
wn
and
p
oin
ts
A
and
B
b
elong
to
line
(
d
)
:
Using
the
protractor,
the
unmark
ed
ruler,
and
without
going
outside
the
frame
of
the
figure,
dra
w
the
image
of
triangle
AB
C
b
y
symmetry
ab
out
axis
(
d
)
..
12.
Axes
of
symmetry
and
bise
ctor
E.5575
Consider
the
figure
b
elo
w
où
the
line
(
d
)
passes
through
the
p
oin
ts
A
and
B
:
h
ttps:/
/c
hingmath.fr
chapExoCorrec/1606
sacados/1606
A
B
(
d
chapExoCorrec/1610
sacados/1610
chapExoCorrec/1613
sacados/1613
chapExoCorrec/1614
sacados/1614
chapExoCorrec/1608
sacados/1608
chapExoCorrec/5577
sacados/5577
(
d
A
B
chapExoCorrec/5575
sacados/5575
A
B
C
(
d
A
B
C
3
cm
40
o
100
o
D
E
F
G
H
1
Dra
w
the
symmetric
of
the
triangle
AB
C
relativ
e
to
the
line
(
d
)
.
2
What
do
es
the
line
(
d
)
represen
t
for
the
angle
∠
B
AB
?
13.
Construction
pr
o
gr
am
and
axis
of
symmetry
E.3065
Consider
the
configuration
b
elo
w
whic
h
admits
the
line
(
AC
)
as
axis
of
symmetry
.
Giv
e
the
plotting
program
for
this
figure.
h
ttps:/
/c
hingmath.fr
chapExoCorrec/3065
sacados/3065
A
B
C
3
cm
40
o
100
o
D
E
F
G
H
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