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

Rajasthan Board RBSE Solutions for Class 7 Maths Chapter 7 Congruence of Triangles Ex 7.2 Textbook Exercise Questions and Answers.

RBSE Class 7 Maths Solutions Chapter 7 Congruence of Triangles Ex 7.2

Question 1. 
Which congruence criterion do you use in the following?
(a) Given : AC = DF
AB = DE 
BC = EF
So, ΔABC ≅ ΔDEF

Answer:
SSS congruence criterion
 
(b) Given : ZX = RP
RQ = ZY 
∠PRQ = ∠XZY 
So, ΔPQR ≅ ΔXYZ

Answer:
SAS congruence criterion

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

Answer:
ASA congruence criterion

(d) Given : EB = DB
AE = BC 
∠A = ∠C = 90°
So, ΔABE ≅ ΔCDB

Answer:
RHS Congruence Criterion 

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 =
Answer:
(i) AR = PE
(ii) RT = EN,
(iii) AT = PN

(b) If it is given that ∠T = ∠N and you are to use SAS criterion, you need to have
(i) RT = and
(ii) PN = 
Answer:
(i) RT = EN
(ii) PN = AT

(c) If it is given that AT = PN and you are to use ASA criterion, you need to have
(i) ? 
(ii) ?
Answer:
(i) ∠ATR = ∠PNE
(ii) ∠TAR = ∠NPE

Question 3.
You have to show that ΔAMP ≅ ΔAMQ.
In the following proof, supply the missing reasons:

Answer:

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:
No, student 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 ΔRAT ≅ ?

Answer:
ΔRAT ≅ ΔWON
(By SAS congruence rule)

Question 6. 
Complete the congruence state¬ment :

Answer:
ΔBCA ≅ ΔBTA (By SSS rule)
ΔQRS ≅ ΔTPQ (By SSS rule)

Question 7.
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 peri¬meters?
Answer:
In a squared sheet, draw ΔABC and ΔPQR.
When two triangles have equal areas and
(i) these triangles are congruent, i.e.
ΔABC ≅ ΔPQR.
(By SSS congruence rule) 
Then, their perimeters are same because length of sides of first triangle are equal to the. length of sides of another triangle by SSS congruence rule.

(ii) But, if the triangles are not congruent, then their perimeters are not same because lengths of sides of first triangle are not equal to the length of corresponding sides of another triangle.

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:

In ΔABC and ΔDEF
AB = DF = 2 cm 
BC = ED = 5 cm 
AC = EF = 3 cm 
∠BAC = ∠EDF 
∠ABC = ∠DEF
But ΔABC is not congruent to ΔDEF.

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

Answer:
BC = QR by ASA congruence rule.

Question 10.
Explain, why ΔABC = ΔFED

Answer:
In ΔABC and ΔFED,
∠ABC = ∠FED = 90°
BC = ED
∠ACB = ∠FDE
(Using angle sum property of a triangle)
∴ ΔABC ≅ ΔFED
(SAS congruence criterion.)