NCERT Solutions for Class 7 Maths Chapter 7 Congruence of Triangles

NCERT Solutions for Class 7 Maths Chapter 7 Congruence of Triangles, are part of NCERT Solutions for Class 7 Maths. Here we have given NCERT Solutions for Class 7 Maths Chapter 7 Congruence of Triangles.

NCERT Solutions for Class 7 Maths Chapter 7 Congruence of Triangles

NCERT Solutions for Class 7 Maths Chapter 7 Congruence of Triangles Ex 7.1

Question 1.
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….

Solution:

(a) Two line segments are congruent if they have the same length.
(b) Among two congruent angles, one has a measure of 70° the measure of the other angle is 70°.
(c) When we write ∠A = ∠B, we actually mean m ∠A = m ∠B.

Question 2.
Give any two real-life examples for congruent shapes.
Solution:
Two one-rupee coins, two ten-rupee notes.

Question 3.
If ∆ ABC = ∆ FED under the correspondence ABC ↔ FED, write all the corresponding congruent parts of the triangles.
Solution:
Corresponding vertices : A and F ; B and E ; C and D.
Corresponding sides : \(\overline { AB } \) and \(\overline { FE } \) ; \(\overline { BC } \) and \(\overline { ED } \); \(\overline { CA } \) and \(\overline { DF } \).
Corresponding angles : ∠A and ∠F ; ∠B and ∠E ; ∠C and ∠D.

Question 4.
If ∆ DEF = ∆ BCA, write the part(s) of ∆ BCA that correspond to

1. ∠E
2. \(\overline { EF } \)
3. ∠F
4. \(\overline { DF } \)

Solution:

1. ∠C
2. \(\overline { CA } \)
3. ∠A
4. \(\overline { BA } \)

NCERT Solutions for Class 7 Maths Chapter 7 Congruence of Triangles Ex 7.2

Question 1.
Which congruence criterion do you use in the following?

Given:
So.
AC = DF
AB = DE
BC = EF
so ∆ ABC = ∆ DEF

Given: ZX = RP
RQ = ZY
∠PRQ = ∠XZY
So, ∆ PQR ≅ ∆ XYZ

Given : ∠MLN = ∠ FGH
∠NML = ∠GFH
ML = GF
So, ∆ LMN ≅ ∆ GFH

Given : EB = DB
AE = BC
∠A = ∠C = 90°
So, ∆ ABE ≅ ∆ CDB
Solution:

(a) SSS congruence criterion
(b) SAS congruence criterion
(c) ASA congruence criterion
(d) RHS congruence criterion.

Question 2.
You want to show that ∆ ART ≅ ∆ PEN,

(а) 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) ?
Solution:

Question 3.
You have to show that ∆ AMP = ∆ AMQ.
In the following proof, supply the missing reasons.


Solution:

Question 4.
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 justified’? Why or why not?
Solution:
No ! he is not justified because AAA is not a criterion for congruence of triangles.

Question 5.
In the figure, the two triangles are congruent. The corresponding parts are marked. We can write ∆ RAT = ?

Solution:
∆ RAT ≅ ∆ WON

Question 6.
Complete the congruence statement:


Solution:
∆ BCA = ∆ BTA
∆ QRS = ∆ TPQ

Question 7.
In a squared sheet, draw two triangles of equal areas such that

1. the triangles are congruent
2. the triangles are not congruent. What can you say about their perimeters?

Solution:

Question 8.
Draw a rough sketch of two triangles such that they have five pairs of congruent parts but still the triangles are not congruent.
Solution:

In ∆ ABC and ∆ DEF,
AB = DF (= 2 cm)
BC = ED (= 4 cm)
CA = EF (= 3 cm)
∠BAC = ∠EDF
∠ABC = ∠DEF
But ∆ ABC is not congruent to ∆ DEF.

Question 9.
If ∆ ABC and ∆ PQR are to be congruent, name one additional pair of corresponding parts. What criterion did you use?

Solution:
BC = RQ by ASA congruence rule.

Question 10.
Explain why ∆ ABC ≅ ∆ FED

Solution:
∠ABC = ∠FED (= 90°) BC = ED
∠ACB = ∠FDE
∵ The sum of the measures of the three angles of a triangle is 180°.
∆ ABC ≅ ∆ FED
By SAS congruence criterion

NCERT Solutions for Class 7 Maths Chapter 7 Congruence of Triangles MCQ

Important Multiple Choice Questions

1. ‘Under a given correspondence, two triangles are congruent if the three sides of the one are equal to the three corresponding sides of the other.’
The above is known as

(a) SSS congruence of two triangles
(b) SAS congruence of two triangles
(c) ASA congruence of two triangles
(d) RHS congruence of two right-angled triangles.

2. ‘Under a given correspondence, two triangles are congruent if two sides and the angle included between them in one of the triangles are equal to the corresponding sides and the angle included between them of the other triangle.’
The above is known as

(a) SSS congruence of two triangles
(b) SAS congruence of two triangles
(c) ASA congruence of two triangles
(d) RHS congruence of two right-angled triangles.

3. ‘Under a given correspondence, two triangles are congruent if two angles and the side included between them in one of the triangles are equal to the corresponding angles and the side included between them of the other triangle.’
The above is known as

(а) SSS congruence of two triangles
(b) SAS congruence of two triangles
(c) ASA congruence of two triangles
(d) RHS congruence of two right-angled triangles.

4. ‘Under a given correspondence, two right-angled triangles are congruent if the hypotenuse and a leg of one of the triangles are equal to the hypotenuse and the corresponding leg of the other triangle.’
The above is known as

(а) SSS congruence of two triangles
(b) SAS congruence of two triangles
(c) ASA congruence of two triangles
(d) RHS congruence of two right-angled triangles.

5. For two given triangles ABC and PQR, how many matchings are possible?

(a) 2
(b) 4
(c) 6
(d) 3.

6. The symbol for congruence is

(a) ≡
(b) ≅
(c) ↔
(d) =

7. The symbol for correspondence is

(a) =
(b) ↔
(c) ≡
(d) ≅.

8. If ∆ ABC = ∆ PQR, then \(\overline { AB } \) corresponds to

(a) \(\overline { PQ } \)
(b) \(\overline { QR } \)
(c) \(\overline { RP } \)
(d) none of these.

9. If ∆ ABC = ∆ PQR, then \(\overline { BC } \) corresponds to

(a) \(\overline { PQ } \)
(b) \(\overline { QR } \)
(c) \(\overline { RP } \)
(d) none of these.

10. If ∆ ABC = ∆ PQR, then \(\overline { CA } \) corresponds to

(a) \(\overline { PQ } \)
(b) \(\overline { QR } \)
(c) \(\overline { RP } \)
(d) none of these.

11. If ∆ ABC = ∆ PQR, then ∠A corresponds to

(a) ∠P
(b) ∠Q
(c) ∠R
(d) none of these.

12. If ∆ ABC = ∆ PQR, then ∠B corresponds to

(a) ∠ P
(b) ∠ Q
(c) ∠ R
(d) none of these.

13. If ∆ ABC= ∆ PQR, then ∠C corresponds to

(a) ∠ P
(b) ∠ Q
(c) ∠ R
(d) none of these.

14. We want to show that ∆ ART = ∆ PEN and we have to use SSS criterion. We have AR = PE and RT = EN. What more we need to show?

(a) AT = PN
(b) AT = PE
(c) AT = EN
(d) none of these.

15. We want to show that ∆ ART = ∆ PEN. We have to use SAS criterion. We have ∠ T = ∠ N, RT = EN. What more we need to show?

(a) PN = AT
(b) PN = AR
(c) PN = RT
(d) None of these.

16. We want to show that ∆ ART = ∆ PEN. We have to use ASA criterion. We have AT = PN, ∠ A = ∠ P. What more we need to show?

(a) ∠T = ∠N
(b) ∠T = ∠E
(c) ∠T = ∠P
(d) None of these.

17. Which congruence criterion do you use in the following?

Given AC = DF
AB = DE
BC = EF
So, ∆ ABC ≅ ∆ DEF

(a) SSS
(b) SAS
(c) ASA
(d) RHS.

18. Which congruence criterion do you use in the following?

Given : ZX = RP
RQ = ZY
∠ PRQ = ∠ XZY
So, ∆ PRQ = ∆ XYZ

(a) SSS
(b) SAS
(c) ASA
(d) RHS.

19. Which congruence criterion do you use in the following?

(a) SSS
(b) SAS
(c) ASA
(d) RHS.

20. Which congruence criterion do you use in the following?

(a) SSS
(b) SAS
(c) ASA
(d) RHS.

21. In the following figure, the two triangles are congruent. The corresponding parts are marked. We can write ∆ RAT = ?

(a) ∆ WON
(b) ∆ WNO
(c) ∆ OWN
(d) ∆ ONW

22. Complete the congruence statement ∆ BCA = ?

(a) ∆ BTA
(b) ∆ BAT
(c) ∆ ABT
(d) ∆ ATB.

23. Complete the congruence statement ∆ QRS

(a) ∆ TPQ
(b) ∆ TQP
(c) ∆ QTP
(d) ∆ QPT.

24. If ∆ ABC and ∆ PQR are to be congruent, name one additional pair of corresponding parts

(a) BC = QR
(b) BC = PQ
(c) BC = PR
(d) none of these.

25. By which congruence, is ∆ ABC = ∆ FED?

(a) SSS
(b) SAS
(c) ASA
(d) RHS.

ANSWERS

HINTS/SOLUTIONS

5. ABC ↔ PQR, ABC ↔ PRQ,
ABC ↔ QRP, ABC ↔ QPR,
ABC ↔ RPQ, ABC ↔ RQP.

25. ∠B = ∠E, BC = ED, ∠D = ∠C
(By angle sum property of a triangle).

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