NCERT Solutions Chapter 7 - Congruence of Triangles, Maths, Class 7 | EduRev Notes

Mathematics (Maths) Class 7

Created by: Praveen Kumar

Class 7 : NCERT Solutions Chapter 7 - Congruence of Triangles, Maths, Class 7 | EduRev Notes

The document NCERT Solutions Chapter 7 - Congruence of Triangles, Maths, Class 7 | EduRev Notes is a part of the Class 7 Course Mathematics (Maths) Class 7.
All you need of Class 7 at this link: Class 7

Exercise 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 70o, the measure of other angle is _______________. 

(c) When we write ∠A = ∠B, we actually mean _______________. 

Answer 1: 

(a) they have the same length

(b) 70o

(c) mA = mB

Question 2: 

Give any two real time examples for congruent shapes. 

Answer 2: 

(i) Two footballs

(ii) Two teacher’s tables

Question 3: 

If ΔABC ≌  ΔFED under the correspondence NCERT Solutions Chapter 7 - Congruence of Triangles, Maths, Class 7 | EduRev Notes, write all the corresponding congruent parts of the triangles.

Answer 3: 

NCERT Solutions Chapter 7 - Congruence of Triangles, Maths, Class 7 | EduRev Notes

Given: ΔABC ≌  ΔFED.

The corresponding congruent parts of die triangles are:

NCERT Solutions Chapter 7 - Congruence of Triangles, Maths, Class 7 | EduRev Notes

Question 4: 

If ΔDEF ≌  ΔBCA, write the part (s) of ΔBCA that correspond to:

NCERT Solutions Chapter 7 - Congruence of Triangles, Maths, Class 7 | EduRev Notes

Answer 4: 

NCERT Solutions Chapter 7 - Congruence of Triangles, Maths, Class 7 | EduRev Notes
NCERT Solutions Chapter 7 - Congruence of Triangles, Maths, Class 7 | EduRev Notes

Exercise 7.2 

Question 1: 

Which congruence criterion do you use in the following? 

(a) Given:    AC = DF, AB = DE, BC = EF
 So    ΔABC ≌  ΔDEF

NCERT Solutions Chapter 7 - Congruence of Triangles, Maths, Class 7 | EduRev Notes

(b) Given:    RP = ZX, RQ = ZY, ∠PRQ = ∠XZY
 So    ΔPQR ≌  ΔXYZ

NCERT Solutions Chapter 7 - Congruence of Triangles, Maths, Class 7 | EduRev Notes

(c) Given:    ∠ MLN = ∠ FGH, ∠ NML = ∠ HFG, ML = FG
 So    ΔLMN ≌ ΔGFH

NCERT Solutions Chapter 7 - Congruence of Triangles, Maths, Class 7 | EduRev Notes

(d) Given:    EB = BD, AE = CB, ∠A = ∠C = 90°
 So    AABE = ACDB

NCERT Solutions Chapter 7 - Congruence of Triangles, Maths, Class 7 | EduRev Notes

Answer 1: 

(a) By SSS congruence criterion,  since it is given that AC = DF, AB = DE, BC = EF
The three sides of one triangle are equal to the three corresponding sides of another triangle.
Therefore, ΔABC ≌  ΔDEF

(b) By SAS congruence criterion,  since it is given that RP = ZX, RQ = ZY and ∠PRQ = ∠XZY
The two sides and one angle in one of the triangle are equal to the corresponding sides and the angle of other triangle.
Therefore, ΔPQR ≌ ΔXYZ

(c) By ASA congruence criterion, since it is given that ∠MLN = ∠FGH, ∠NML = ∠HFG, ML = FG.
The two angles and one side in one of the triangle are equal to the corresponding angles and side of other triangle.
Therefore, ΔLMN ≌  ΔGFH

(d) By RHS congruence criterion, since it is given that EB = BD, AE = CB, ∠A = ∠C = 90°
Hypotenuse and one side of a right angled triangle are respectively equal to the hypotenuse and one side of another right angled triangle.
Therefore, ΔABE ≌  ΔCDB

Question 2: 

You want to show that ΔART ≌  ΔPEN:
 (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) ?

NCERT Solutions Chapter 7 - Congruence of Triangles, Maths, Class 7 | EduRev Notes

Answer 2: 

(a) Using SSS criterion,    ΔART ≌  ΔPEN
(i) AR = PE    
(ii) RT= EN    
(iii) AT = PN

(b) Given: ∠T = ∠N
Using SAS criterion,    ΔART ≌  ΔPEN
(i) RT = EN    
(ii) PN = AT

(c) Given:  AT = PN
Using ASA criterion,    ΔART ≌  ΔPEN
(i) ∠RAT = ∠EPN    
(ii) ∠RTA = ∠ENP

Question 3: 

You have to show that ΔAMP = ΔAMQ. In the following proof supply the missing reasons:

NCERT Solutions Chapter 7 - Congruence of Triangles, Maths, Class 7 | EduRev Notes

Steps

Reasons

(i) PM = QM

(i)

(ii) ∠ PMA = ∠ QMA

(ii)

(iii) AM = AM

(iii)

(iv) ΔAMP ≌ ΔAMQ

(iv)

 

Answer 3: 

Steps

Reasons

(i) PM = QM

(i) Given

(ii) ∠PMA = ∠QMA

(ii) Given

(iii) AM = AM

(iii) Common

(iv) Δ AMP ≌ ΔAMQ

(iv) SAS congruence rule

 

Question 4: 

In ΔABC, ∠A = 30% ∠B = 40° and ∠C = 110°
 In ΔPQR, ∠P = 30% ∠Q = 40° and ∠R = 110°.
 A student says that ΔABC ≌ ΔPQR by AAA congruence criterion. Is he justified? Why or why not?

Answer 4: 

No, because the two triangles with equal corresponding angles need not be congruent. In such a correspondence, one of them can be an enlarged copy of the other.

Question 5:

In the figure, the two triangles are congruent. The corresponding parts are marked. We can write Δ RAT ≌ ?

NCERT Solutions Chapter 7 - Congruence of Triangles, Maths, Class 7 | EduRev Notes

Answer 5: 

In the figure, given two triangles are congruent. So, the corresponding parts are:

NCERT Solutions Chapter 7 - Congruence of Triangles, Maths, Class 7 | EduRev Notes

We can write, ΔRAT ≌ ΔWON    [By SAS congruence rule]

Question 6: 

Complete the congruence statement:

NCERT Solutions Chapter 7 - Congruence of Triangles, Maths, Class 7 | EduRev Notes

Answer 6: 

In A BAT and ABAC, given triangles are congruent so the corresponding parts are:

NCERT Solutions Chapter 7 - Congruence of Triangles, Maths, Class 7 | EduRev Notes

Thus, ΔBCA ≌ ΔBTA    |By SSS congruence rule]
In ΔQRS and ΔTPQ, given triangles are congruent so the corresponding parts are:

NCERT Solutions Chapter 7 - Congruence of Triangles, Maths, Class 7 | EduRev Notes

Thus, ΔQRS ≌  ΔTPQ    [By SSS congruence rule]

Question 7: 

In a squared sheet, draw two triangles of equal area such that: 

(i) the triangles are congruent. 

(ii) the triangles are not congruent. 

What can you say about their perimeters? 

Answer 7: 

In a squared sheet, draw ΔABC and ΔPQR. When two triangles have equal areas and

(i)
NCERT Solutions Chapter 7 - Congruence of Triangles, Maths, Class 7 | EduRev Notes

In the above figure, ΔABC and ΔDEF have equal areas.
And also, NCERT Solutions Chapter 7 - Congruence of Triangles, Maths, Class 7 | EduRev Notes ΔDEF
So, we can say that perimeters of ΔABC and ΔDEF are equal. 


(ii)
NCERT Solutions Chapter 7 - Congruence of Triangles, Maths, Class 7 | EduRev Notes
In the above figure, ΔLMN and ΔOPQ
ΔLMN is not congruent to ΔOPQ
So, we can also say that their perimeters are not same.

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. 

Answer 8: 

Let us draw two triangles PQR and ABC.

NCERT Solutions Chapter 7 - Congruence of Triangles, Maths, Class 7 | EduRev Notes

All angles are equal, two sides are equal except one side. Hence, ΔPQR are not congruent to ΔABC.

Question 9: 

If ΔABC and ΔPQR are to be congruent, name one additional pair of corresponding parts. What criterion did you use? 

NCERT Solutions Chapter 7 - Congruence of Triangles, Maths, Class 7 | EduRev Notes

Answer 9: 

A ABC and A PQR are congruent Then one additional pair is NCERT Solutions Chapter 7 - Congruence of Triangles, Maths, Class 7 | EduRev Notes

Given: ∠B = ∠Q = 90°

NCERT Solutions Chapter 7 - Congruence of Triangles, Maths, Class 7 | EduRev Notes

Therefore, ΔABC ≌ ΔPQR    [By ASA congruence rule]

Question 10: 

Explain, why ΔABC  ΔFED.

NCERT Solutions Chapter 7 - Congruence of Triangles, Maths, Class 7 | EduRev NotesNCERT Solutions Chapter 7 - Congruence of Triangles, Maths, Class 7 | EduRev Notes

Answer 10: 

Given:    ∠A = ∠F, BC = ED, ∠B = ∠E
 In ΔABC and ΔFED,
 ∠B = ∠E = 90°
 ∠A = ∠F
 BC = ED
 Therefore, ΔABC ≌ ΔFED    [By RHS congruence rule]

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