NCERT Solutions for Class 7 Maths Congruence of Triangles [Old Book]
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Book Name: Maths
Subject: Maths
Chapter Number: 7
Chapter Name: Congruence of Triangles
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Book Name: Maths
Subject: Maths
Chapter Number: 7
Chapter Name: Congruence of Triangles
You can also bookmark this page by clicking + Save to Library icon and refer to these NCERT Solutions anytime from your account. More Detail
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Page 1
NCERT
SOLUTIONS
CLASS - 7TH
aglase .co
SOLUTIONS
CLASS - 7TH
aglase .co
Page 2
Book : Mathematics Ncert Solutions | Chapter-7 Maths
Class : 7th
Subject : Maths
Chapter : 7
Chapter Name : Congruence of Triangles
Exercise 7.1
Q1 Complete the following statements:
(a) Two line segments are congruent if ___________.
(b) Among two congruent angles, one has a measure of 70°; the measure of the other angle is
___________.
(c) When we write ∠A = ∠B, we actually mean ___________.
Answer. (a) They have the same length
(b) 70°
(c) m ∠A = m ∠B
Page : 138 , Block Name : Exercise 7.1
Q2 Give any two real-life examples for congruent shapes.
Answer. (i) Sheets of same letter pad
(ii) Biscuits in the same packet
Page : 138 , Block Name : Exercise 7.1
Q3 If ∆ABC ≅ ∆FED under the correspondence ABC ↔ FED, write all the corresponding
congruent parts of the triangles.
Answer. If these triangles are congruent, then the corresponding angles and sides will be equal
to each other.
∠A ↔ ∠F
∠B ↔ ∠E
∠C ↔ ∠D
¯¯¯¯¯¯¯¯ ¯¯¯¯¯¯¯¯
BC ↔ F E
¯¯¯¯¯¯¯¯ ¯
¯¯¯
¯¯¯
¯¯
BC ↔ ED
¯¯¯¯¯¯¯¯ ¯
¯¯¯
¯¯¯
¯¯
CA ↔ DF
Page 1 of 7 Aglasem Schools
Class : 7th
Subject : Maths
Chapter : 7
Chapter Name : Congruence of Triangles
Exercise 7.1
Q1 Complete the following statements:
(a) Two line segments are congruent if ___________.
(b) Among two congruent angles, one has a measure of 70°; the measure of the other angle is
___________.
(c) When we write ∠A = ∠B, we actually mean ___________.
Answer. (a) They have the same length
(b) 70°
(c) m ∠A = m ∠B
Page : 138 , Block Name : Exercise 7.1
Q2 Give any two real-life examples for congruent shapes.
Answer. (i) Sheets of same letter pad
(ii) Biscuits in the same packet
Page : 138 , Block Name : Exercise 7.1
Q3 If ∆ABC ≅ ∆FED under the correspondence ABC ↔ FED, write all the corresponding
congruent parts of the triangles.
Answer. If these triangles are congruent, then the corresponding angles and sides will be equal
to each other.
∠A ↔ ∠F
∠B ↔ ∠E
∠C ↔ ∠D
¯¯¯¯¯¯¯¯ ¯¯¯¯¯¯¯¯
BC ↔ F E
¯¯¯¯¯¯¯¯ ¯
¯¯¯
¯¯¯
¯¯
BC ↔ ED
¯¯¯¯¯¯¯¯ ¯
¯¯¯
¯¯¯
¯¯
CA ↔ DF
Page 1 of 7 Aglasem Schools
Page 3
Book : Mathematics Ncert Solutions | Chapter-7 Maths
Page : 138 , Block Name : Exercise 7.1
Q4 If ∆DEF ≅ ∆BCA, write the part(s) of ∆BCA that correspond to
(i) ∠E
(ii)EF
¯¯¯¯¯¯¯
(iii) ∠F (iv) DF
¯
¯¯¯
¯¯¯¯
Answer. (i) ∠C
(ii)CA
¯¯
¯¯¯
¯¯¯
(iii) ∠A
(iv) BA
¯¯
¯¯¯
¯¯¯
Page : 138 , Block Name : Exercise 7.1
Exercise 7.2
Q1 Which congruence criterion do you use in the following?
(a) Given: AC = DF
AB = DE
BC = EF So, ∆ABC ≅ ∆DEF
(b) Given: ZX = RP
RQ = ZY
∠PRQ = ∠XZY
So, ∆PQR ≅ ∆XYZ
(c) Given: ∠MLN = ∠FGH
∠NML = ∠GFH
ML = FG
So, ∆LMN ≅ ∆GFH
Page 2 of 7 Aglasem Schools
Page : 138 , Block Name : Exercise 7.1
Q4 If ∆DEF ≅ ∆BCA, write the part(s) of ∆BCA that correspond to
(i) ∠E
(ii)EF
¯¯¯¯¯¯¯
(iii) ∠F (iv) DF
¯
¯¯¯
¯¯¯¯
Answer. (i) ∠C
(ii)CA
¯¯
¯¯¯
¯¯¯
(iii) ∠A
(iv) BA
¯¯
¯¯¯
¯¯¯
Page : 138 , Block Name : Exercise 7.1
Exercise 7.2
Q1 Which congruence criterion do you use in the following?
(a) Given: AC = DF
AB = DE
BC = EF So, ∆ABC ≅ ∆DEF
(b) Given: ZX = RP
RQ = ZY
∠PRQ = ∠XZY
So, ∆PQR ≅ ∆XYZ
(c) Given: ∠MLN = ∠FGH
∠NML = ∠GFH
ML = FG
So, ∆LMN ≅ ∆GFH
Page 2 of 7 Aglasem Schools
Page 4
Book : Mathematics Ncert Solutions | Chapter-7 Maths
(d) Given: EB = DB
AE = BC
∠A = ∠C = 90°
So, ∆ABE ≅ ∆CDB
Answer. (a) SSS, as the sides of /ABC are equal to the sides of /DEF.
(b) SAS, as two sides and the angle included between these sides of /PQR are equal to two
sides and the angle included between these sides of /XYZ.
(c) ASA, as two angles and the side included between these angles of /LMN are equal to two
angles and the side included between these angles of /GFH.
(d) RHS, as in the given two right-angled triangles, one side and the hypotenuse are
respectively equal.
Page : 149 , Block Name : Exercise 7.2
Q2 You want to show that ∆ART ≅ ∆PEN,
(a) If you have to use SSS criterion, then you need to show
(i) AR = (ii) RT = (iii) AT =
(b) If it is given that ∠T = ∠N and you are to use SAS criterion, you need to have
(i) RT = and (ii) PN =
(c) If it is given that AT = PN and you are to use ASA criterion, you need to have
(i) ? (ii) ?
Answer. (a)
(i) AR = PE
(ii) RT = EN
(iii) AT = PN
Page 3 of 7 Aglasem Schools
(d) Given: EB = DB
AE = BC
∠A = ∠C = 90°
So, ∆ABE ≅ ∆CDB
Answer. (a) SSS, as the sides of /ABC are equal to the sides of /DEF.
(b) SAS, as two sides and the angle included between these sides of /PQR are equal to two
sides and the angle included between these sides of /XYZ.
(c) ASA, as two angles and the side included between these angles of /LMN are equal to two
angles and the side included between these angles of /GFH.
(d) RHS, as in the given two right-angled triangles, one side and the hypotenuse are
respectively equal.
Page : 149 , Block Name : Exercise 7.2
Q2 You want to show that ∆ART ≅ ∆PEN,
(a) If you have to use SSS criterion, then you need to show
(i) AR = (ii) RT = (iii) AT =
(b) If it is given that ∠T = ∠N and you are to use SAS criterion, you need to have
(i) RT = and (ii) PN =
(c) If it is given that AT = PN and you are to use ASA criterion, you need to have
(i) ? (ii) ?
Answer. (a)
(i) AR = PE
(ii) RT = EN
(iii) AT = PN
Page 3 of 7 Aglasem Schools
Page 5
Book : Mathematics Ncert Solutions | Chapter-7 Maths
(b) (i) RT = EN
(ii) PN = AT
(c) (i) ∠ATR = ∠PNE
(ii) ∠RAT = ∠EPN
Page : 149 , Block Name : Exercise 7.2
Q3 You have to show that ∆AMP ≅ ∆AMQ. In the following proof, supply the missing reasons.
Answer. (i) Given
(ii) Given
(iii) Common
(iv) SAS, as the two sides and the angle included between these sides of /AMP are equal to two
sides and the angle included between these sides of /AMQ.
Q4 In ∆ABC, ∠A = 30° , ∠B = 40° and ∠C = 110°
In ∆PQR, ∠P = 30° , ∠Q = 40° and ∠R = 110° /
A student says that ∆ABC ≅ ∆PQR by AAA congruence criterion. Is he justi ed? Why or why
not?
Answer. No. This property represents that these triangles have their respective angles of equal
measure. However, this gives no information about their sides. The sides of these triangles
have a ratio somewhat different than 1:1. Therefore, AAA property does not prove the two
triangles congruent.
Q5 In the gure, the two triangles are congruent. The corresponding parts are marked. We can
write ∆RAT ≅ ?
Answer. It can be observed that,
∠RAT = ∠WON
Page 4 of 7 Aglasem Schools
(b) (i) RT = EN
(ii) PN = AT
(c) (i) ∠ATR = ∠PNE
(ii) ∠RAT = ∠EPN
Page : 149 , Block Name : Exercise 7.2
Q3 You have to show that ∆AMP ≅ ∆AMQ. In the following proof, supply the missing reasons.
Answer. (i) Given
(ii) Given
(iii) Common
(iv) SAS, as the two sides and the angle included between these sides of /AMP are equal to two
sides and the angle included between these sides of /AMQ.
Q4 In ∆ABC, ∠A = 30° , ∠B = 40° and ∠C = 110°
In ∆PQR, ∠P = 30° , ∠Q = 40° and ∠R = 110° /
A student says that ∆ABC ≅ ∆PQR by AAA congruence criterion. Is he justi ed? Why or why
not?
Answer. No. This property represents that these triangles have their respective angles of equal
measure. However, this gives no information about their sides. The sides of these triangles
have a ratio somewhat different than 1:1. Therefore, AAA property does not prove the two
triangles congruent.
Q5 In the gure, the two triangles are congruent. The corresponding parts are marked. We can
write ∆RAT ≅ ?
Answer. It can be observed that,
∠RAT = ∠WON
Page 4 of 7 Aglasem Schools
Page 6
Book : Mathematics Ncert Solutions | Chapter-7 Maths
∠ART = ∠OWN
AR = OW
Therefore, /RAT /WON, by ASA criterion.
Q6 Complete the congruence statement:
Answer. Given that, BC = BT
TA = CA
BA is common.
Therefore, /BCA /BTA
Similarly, PQ = RS
TQ = QS
PT = RQ
Therefore, /QRS /TPQ
Q7 In a squared sheet, draw two triangles of equal areas such that :
(i) the triangles are congruent.
(ii) the triangles are not congruent.
What can you say about their perimeters?
Answer. (i)
Here, /ABC and /PQR have the same area and are congruent to each other also. Also, the
perimeter of both the triangles will be the same.
(ii)
Page 5 of 7 Aglasem Schools
∠ART = ∠OWN
AR = OW
Therefore, /RAT /WON, by ASA criterion.
Q6 Complete the congruence statement:
Answer. Given that, BC = BT
TA = CA
BA is common.
Therefore, /BCA /BTA
Similarly, PQ = RS
TQ = QS
PT = RQ
Therefore, /QRS /TPQ
Q7 In a squared sheet, draw two triangles of equal areas such that :
(i) the triangles are congruent.
(ii) the triangles are not congruent.
What can you say about their perimeters?
Answer. (i)
Here, /ABC and /PQR have the same area and are congruent to each other also. Also, the
perimeter of both the triangles will be the same.
(ii)
Page 5 of 7 Aglasem Schools
Page 7
Book : Mathematics Ncert Solutions | Chapter-7 Maths
Here, the two triangles have the same height and base. Thus, their areas are equal. However,
these triangles are not congruent to each other. Also, the perimeter of both the triangles will
not be the same.
Q8 Draw a rough sketch of two triangles such that they have ve pairs of congruent parts but
still the triangles are not congruent.
Answer. In some special cases (which depend on the lengths of the sides and the size of the
angle involved),
SSA is enough to show congruence. However, it is not always enough. Consider the following
triangles :
Here side AB is congruent to side DE (S) side AC is congruent to side DF(S) angle C is
congruent to angle F(A)
But the triangles are not congruent, as we can see.
What happens is this : If we draw a vertical line through point A in the rst triangle, we can
sort of “ ip” side AB around this line to get the second triangle. If we were to lay one triangle
on top of the other and draw the vertical line, this how it would look.
Clearly, side DE is just side AB ipped around the line. So, we have not changed the length of
the side, and the other side AC (or DF) is unchanged, as is angle C (or F). So, these two
triangles that have the same SSA information, but they are not congruent.
Q9 If ∆ABC and ∆PQR are to be congruent, name one additional pair of corresponding parts.
What criterion did you use?
Answer. BC = QR
Page 6 of 7 Aglasem Schools
Here, the two triangles have the same height and base. Thus, their areas are equal. However,
these triangles are not congruent to each other. Also, the perimeter of both the triangles will
not be the same.
Q8 Draw a rough sketch of two triangles such that they have ve pairs of congruent parts but
still the triangles are not congruent.
Answer. In some special cases (which depend on the lengths of the sides and the size of the
angle involved),
SSA is enough to show congruence. However, it is not always enough. Consider the following
triangles :
Here side AB is congruent to side DE (S) side AC is congruent to side DF(S) angle C is
congruent to angle F(A)
But the triangles are not congruent, as we can see.
What happens is this : If we draw a vertical line through point A in the rst triangle, we can
sort of “ ip” side AB around this line to get the second triangle. If we were to lay one triangle
on top of the other and draw the vertical line, this how it would look.
Clearly, side DE is just side AB ipped around the line. So, we have not changed the length of
the side, and the other side AC (or DF) is unchanged, as is angle C (or F). So, these two
triangles that have the same SSA information, but they are not congruent.
Q9 If ∆ABC and ∆PQR are to be congruent, name one additional pair of corresponding parts.
What criterion did you use?
Answer. BC = QR
Page 6 of 7 Aglasem Schools
Page 8
Book : Mathematics Ncert Solutions | Chapter-7 Maths
/ABC /PQR (ASA criterion)
Q10 Explain, why ∆ABC ≅ ∆FED.
Answer. Given that, ∠ABC = ∠FED (1)
∠BAC = ∠EFD (2)
The two angles of /ABC are equal to the two respective angles of /FED. Also, the sum of all
interior angles of a triangle is 180º. Therefore, third angle of both triangles will also be equal
in measure.
∠BCA = ∠EDF (3)
Page : 151 , Block Name : Exercise 7.2
Page 7 of 7 Aglasem Schools
/ABC /PQR (ASA criterion)
Q10 Explain, why ∆ABC ≅ ∆FED.
Answer. Given that, ∠ABC = ∠FED (1)
∠BAC = ∠EFD (2)
The two angles of /ABC are equal to the two respective angles of /FED. Also, the sum of all
interior angles of a triangle is 180º. Therefore, third angle of both triangles will also be equal
in measure.
∠BCA = ∠EDF (3)
Page : 151 , Block Name : Exercise 7.2
Page 7 of 7 Aglasem Schools
Document Details
| Board / Org | NCERT |
| Exam | Class 7 |
| Type | Solution |
| Pages | 8 |
| Updated | 30 Apr 2026 |