Class 7
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Mathematics
Geometric Twins
NCERT Solutions
NCERT Solutions
Geometric Twins
35 Solutions
Exercise:
All Exercises
Figure it Out 1
Figure it Out 1.1
Figure it Out 1.2
Figure it Out 1.3
Figure it Out 1.4
Figure it Out 2
Figure it Out 3
Figure it Out 4
Q1
Figure it Out 1
Check if the two figures are congruent.
Q2
Figure it Out 1
Circle the pairs that appear congruent.
Q3
Figure it Out 1
What measurements would you take to create a figure congruent to a given:
(a)
Circle
(b)
Rectangle
Using this, state how would you check if two -
(a)
Circles are congruent?
(b)
Rectangles are congruent?
Q4
Figure it Out 1
How would we check if two figures like the one below are congruent? Use this to identify whether each of the following pairs are congruent.
Q1
Figure it Out 1.1
Check if the two figures are congruent.
Q2
Figure it Out 1.1
Circle the pairs that appear congruent.
Q3
Figure it Out 1.1
What measurements would you take to create a figure congruent to a given:
(a)
Circle
(b)
Rectangle
Using this, state how would you check if two -
(a)
Circles are congruent?
(b)
Rectangles are congruent?
Q4
Figure it Out 1.1
How would we check if two figures like the one below are congruent? Use this to identify whether each of the following pairs are congruent.
Q1
Figure it Out 1.2
Suppose
△
H
E
N
\triangle \mathrm{HEN}
△
HEN
is congruent to
△
B
I
G
\triangle \mathrm{BIG}
△
BIG
. List all the other correct ways of expressing this congruence.
Q3
Figure it Out 1.2
In the figure below,
A
B
=
A
D
,
C
B
=
C
D
\mathrm{AB}=\mathrm{AD}, \mathrm{CB}=\mathrm{CD}
AB
=
AD
,
CB
=
CD
.
Can you identify any pair of congruent triangles? If yes, explain why they are congruent. Does AC divide
∠
B
A
D
\angle \mathrm{BAD}
∠
BAD
and
∠
B
C
D
\angle \mathrm{BCD}
∠
BCD
into two equal parts? Give reasons.
Q4
Figure it Out 1.2
In the figure below, are
△
D
F
E
\triangle \mathrm{DFE}
△
DFE
and
△
G
E
D
\triangle \mathrm{GED}
△
GED
congruent to each other? It is given that
D
F
=
D
G
\mathrm{DF}=\mathrm{DG}
DF
=
DG
and
F
E
=
G
E
\mathrm{FE}=\mathrm{GE}
FE
=
GE
.
Q1
Figure it Out 1.3
Identify whether the triangles below are congruent. What conditions did you use to establish their congruence? Express the congruence.
Q2
Figure it Out 1.3
Given that CD and AB are parallel, and
A
B
=
C
D
\mathrm{AB}=\mathrm{CD}
AB
=
CD
, what are the other equal parts in this figure? (Hint: When the lines are parallel, the alternate angles are equal. Are the two resulting triangles congruent? If so, express the congruence.)
Q3
Figure it Out 1.3
Given that
∠
A
B
C
=
∠
D
B
C
\angle \mathrm{ABC}=\angle \mathrm{DBC}
∠
ABC
=
∠
DBC
and
∠
A
C
B
=
∠
D
C
B
\angle \mathrm{ACB}=\angle \mathrm{DCB}
∠
ACB
=
∠
DCB
, show that
∠
B
A
C
=
∠
B
D
C
\angle \mathrm{BAC}=\angle \mathrm{BDC}
∠
BAC
=
∠
BDC
. Are the two triangles congruent?
Q4
Figure it Out 1.3
Identify the equal parts in the following figure, given that
∠
A
B
D
=
∠
D
C
A
\angle \mathrm{ABD}= \angle \mathrm{DCA}
∠
ABD
=
∠
DCA
and
∠
A
C
B
=
∠
D
B
C
\angle \mathrm{ACB}=\angle \mathrm{DBC}
∠
ACB
=
∠
DBC
.
Q1
Figure it Out 1.4
△
A
I
R
≅
△
F
L
Y
\triangle \mathrm{AIR} \cong \triangle \mathrm{FLY}
△
AIR
≅
△
FLY
. Identify the corresponding vertices, sides and angles.
Q2
Figure it Out 1.4
Each of the following cases contains certain measurements taken from two triangles. Identify the pairs in which the triangles are congruent to each other, with reason. Express the congruence whenever they are congruent.
(a)
A
B
=
D
E
\mathrm{AB}=\mathrm{DE}
AB
=
DE
B
C
=
E
F
\mathrm{BC}=\mathrm{EF}
BC
=
EF
C
A
=
D
F
\mathrm{CA}=\mathrm{DF}
CA
=
DF
(b)
A
B
=
E
F
\mathrm{AB}=\mathrm{EF}
AB
=
EF
∠
A
=
∠
E
\angle \mathrm{A}=\angle \mathrm{E}
∠
A
=
∠
E
A
C
=
E
D
\mathrm{AC}=\mathrm{ED}
AC
=
ED
(c)
A
B
=
D
F
\mathrm{AB}=\mathrm{DF}
AB
=
DF
∠
B
=
∠
D
=
90
∘
\angle \mathrm{B}=\angle \mathrm{D}=90^{\circ}
∠
B
=
∠
D
=
9
0
∘
A
C
=
F
E
\mathrm{AC}=\mathrm{FE}
AC
=
FE
(d)
∠
A
=
∠
D
\angle \mathrm{A}=\angle \mathrm{D}
∠
A
=
∠
D
∠
B
=
∠
E
\angle \mathrm{B}=\angle \mathrm{E}
∠
B
=
∠
E
A
C
=
D
F
\mathrm{AC}=\mathrm{DF}
AC
=
DF
(e)
A
B
=
D
F
\mathrm{AB}=\mathrm{DF}
AB
=
DF
∠
B
=
∠
F
\angle \mathrm{B}=\angle \mathrm{F}
∠
B
=
∠
F
A
C
=
D
E
\mathrm{AC}=\mathrm{DE}
AC
=
DE
Q3
Figure it Out 1.4
It is given that
O
B
=
O
C
\mathrm{OB}=\mathrm{OC}
OB
=
OC
, and
O
A
=
O
D
\mathrm{OA}=\mathrm{OD}
OA
=
OD
. Show that AB is parallel to CD. [Hint: AD is a transversal for these two lines. Are there any equal alternate angles?]
Q4
Figure it Out 1.4
ABCD is a square. Show that
△
A
B
C
≅
△
A
D
C
\triangle \mathrm{ABC} \cong \triangle \mathrm{ADC}
△
ABC
≅
△
ADC
. Is
△
A
B
C
\triangle \mathrm{ABC}
△
ABC
also congruent to
△
C
D
A
\triangle \mathrm{CDA}
△
CDA
? Give more examples of two triangles where one triangle is congruent to the other in two different ways, as in the case above. Can you give an example of two triangles where one is congruent to the other in six different ways?
Q5
Figure it Out 1.4
Find
∠
B
\angle \mathrm{B}
∠
B
and
∠
C
\angle \mathrm{C}
∠
C
, if A is the centre of the circle.
Q6
Figure it Out 1.4
Find the missing angles. As per the convention that we have been following, all line segments marked with a single '|' are equal to each other and those marked with a double '|' are equal to each other, etc.
Q1
Figure it Out 2
Suppose
△
H
E
N
\triangle \mathrm{HEN}
△
HEN
is congruent to
△
B
I
G
\triangle \mathrm{BIG}
△
BIG
. List all the other correct ways of expressing this congruence.
Q2
Figure it Out 2
Determine whether the triangles are congruent. If yes, express the congruence.
Q3
Figure it Out 2
In the figure below,
A
B
=
A
D
,
C
B
=
C
D
\mathrm{AB}=\mathrm{AD}, \mathrm{CB}=\mathrm{CD}
AB
=
AD
,
CB
=
CD
. Can you identify any pair of congruent triangles? If yes, explain why they are congruent. Does AC divide
∠
B
A
D
\angle \mathrm{BAD}
∠
BAD
and
∠
B
C
D
\angle \mathrm{BCD}
∠
BCD
into two equal parts? Give reasons.
Q4
Figure it Out 2
In the figure below, are
△
D
F
E
\triangle \mathrm{DFE}
△
DFE
and
△
G
E
D
\triangle \mathrm{GED}
△
GED
congruent to each other? It is given that
D
F
=
D
G
\mathrm{DF}=\mathrm{DG}
DF
=
DG
and
F
E
=
G
E
\mathrm{FE}=\mathrm{GE}
FE
=
GE
.
Q1
Figure it Out 3
Identify whether the triangles below are congruent. What conditions did you use to establish their congruence? Express the congruence.
Q2
Figure it Out 3
Given that CD and AB are parallel, and
A
B
=
C
D
\mathrm{AB}=\mathrm{CD}
AB
=
CD
, what are the other equal parts in this figure? (Hint: When the lines are parallel, the alternate angles are equal. Are the two resulting triangles congruent? If so, express the congruence.)
Q3
Figure it Out 3
Given that
∠
A
B
C
=
∠
D
B
C
\angle \mathrm{ABC}=\angle \mathrm{DBC}
∠
ABC
=
∠
DBC
and
∠
A
C
B
=
∠
D
C
B
\angle \mathrm{ACB}=\angle \mathrm{DCB}
∠
ACB
=
∠
DCB
, show that
∠
B
A
C
=
∠
B
D
C
\angle \mathrm{BAC}=\angle \mathrm{BDC}
∠
BAC
=
∠
BDC
. Are the two triangles congruent?
Q4
Figure it Out 3
Identify the equal parts in the following figure, given that
∠
A
B
D
=
∠
D
C
A
\angle \mathrm{ABD}= \angle \mathrm{DCA}
∠
ABD
=
∠
DCA
and
∠
A
C
B
=
∠
D
B
C
\angle \mathrm{ACB}=\angle \mathrm{DBC}
∠
ACB
=
∠
DBC
.
Q1
Figure it Out 4
△
A
I
R
≅
△
F
L
Y
\triangle \mathrm{AIR} \cong \triangle \mathrm{FLY}
△
AIR
≅
△
FLY
. Identify the corresponding vertices, sides and angles.
Q2
Figure it Out 4
Each of the following cases contains certain measurements taken from two triangles. Identify the pairs in which the triangles are congruent to each other, with reason. Express the congruence whenever they are congruent.
(a)
A
B
=
D
E
\mathrm{AB}=\mathrm{DE}
AB
=
DE
,
B
C
=
E
F
\mathrm{BC}=\mathrm{EF}
BC
=
EF
,
C
A
=
D
F
\mathrm{CA}=\mathrm{DF}
CA
=
DF
(b)
A
B
=
E
F
\mathrm{AB}=\mathrm{EF}
AB
=
EF
,
∠
A
=
∠
E
\angle \mathrm{A}=\angle \mathrm{E}
∠
A
=
∠
E
,
A
C
=
E
D
\mathrm{AC}=\mathrm{ED}
AC
=
ED
(c)
A
B
=
D
F
\mathrm{AB}=\mathrm{DF}
AB
=
DF
,
∠
B
=
∠
D
=
90
∘
\angle \mathrm{B}=\angle \mathrm{D}=90^{\circ}
∠
B
=
∠
D
=
9
0
∘
,
A
C
=
F
E
\mathrm{AC}=\mathrm{FE}
AC
=
FE
(d)
∠
A
=
∠
D
\angle \mathrm{A}=\angle \mathrm{D}
∠
A
=
∠
D
,
∠
B
=
∠
E
\angle \mathrm{B}=\angle \mathrm{E}
∠
B
=
∠
E
,
A
C
=
D
F
\mathrm{AC}=\mathrm{DF}
AC
=
DF
(e)
A
B
=
D
F
\mathrm{AB}=\mathrm{DF}
AB
=
DF
,
∠
B
=
∠
F
\angle \mathrm{B}=\angle \mathrm{F}
∠
B
=
∠
F
,
A
C
=
D
E
\mathrm{AC}=\mathrm{DE}
AC
=
DE
Q3
Figure it Out 4
It is given that
O
B
=
O
C
\mathrm{OB}=\mathrm{OC}
OB
=
OC
, and
O
A
=
O
D
\mathrm{OA}=\mathrm{OD}
OA
=
OD
. Show that AB is parallel to CD . [Hint: AD is a transversal for these two lines. Are there any equal alternate angles?]
Q4
Figure it Out 4
ABCD is a square. Show that
△
A
B
C
≅
△
A
D
C
\triangle \mathrm{ABC} \cong \triangle \mathrm{ADC}
△
ABC
≅
△
ADC
. Is
△
A
B
C
\triangle \mathrm{ABC}
△
ABC
also congruent to
△
C
D
A
\triangle \mathrm{CDA}
△
CDA
? Give more examples of two triangles where one triangle is congruent to the other in two different ways, as in the case above. Can you give an example of two triangles where one is congruent to the other in six different ways?
Q5
Figure it Out 4
Find
∠
B
\angle \mathrm{B}
∠
B
and
∠
C
\angle \mathrm{C}
∠
C
, if A is the centre of the circle.
Q6
Figure it Out 4
Find the missing angles. As per the convention that we have been following, all line segments marked with a single '|' are equal to each other and those marked with a double '|' are equal to each other, etc.
More from this chapter
Chapter overview
Important Points
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