EXERCISE 7.2

1) Which congruence criteria do you use in the following
a) Given AC = DF
AB = EF
BC = EF
So, ∆ABC ≅ ∆DEF
Ans: The three side of ∆ABC are equal to the three corresponding sides of ∆DEF,
∴ ∆ABC ≅ ∆DEF by S.S.S Congruence Criteria.

b) Given: ZX = RP

RQ = ZY
∠PRQ = ∠XYZ
So, ∆ PQR ≅ ∆XYZ
Ans: Two sides and the angle between them of ∆ PQR is equal to the corresponding two sides and the angle between then of ∆XYZ.
∴∆ PQR≅∆ XYZ by S.A.S Congruence Criteria.

c) Given: ∠MLN = ∠FGH

ML = FG
So, ∆LMN ≅ ∆GFH
Ans: Two angles and the included side of ∆LMN is equal to the corresponding two angles and included side of ∆GFH
∴ ∆LMN  ∆GFH by A.S.A Congruence Criteria

d) Given : EB = DB
AE = BC
∠A = ∠C = 90°
So ∆ ABE ≅ ∆ CDB
Ans: The hypotenuse and one side of ∆ ABE is equal to the corresponding hypotenuse and one side of ∆ COB
∴ ∆ ABE ≅ ∆ COB by RHS Congruence Criteria

2) You want to show that ∆ ART ≅ ∆ PEN,

a) If you have to use S.S.S Criteria, then you need to show
i) AR = ii) RT = iii) AT =
Ans: i) PE      ii) EN          iii) PN

b) If it is given that ∠T = ∠N and you are to use S.A.S Criteria, you need to have
i) RT = and ii) PN =
Ans: i) EN      ii) AT

c) If it is given that AT = PN and you are to use A.S.A Criteria, you need to have   i) ? ii) ?
Ans: i) ∠ RAT = ∠EPN       ii) ∠ ATR = ∠ PNT

3). You have to show that ∆ AMP ≅ ∆ AMQ
In the following proof, supply the missing reasons.
 Reasons:

Steps Reasons
(i) PM = QM (i) …
(ii) ∠PMA = ∠QMA (ii) …
(iii) AM = AM (iii) …
(iv) ΔAMP ≅ ΔAMQ (iv) …

Ans: i) From the given figure   ii) From the given figure
iii) Common side      iv) S.A.S Congruence Criteria

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 A.A.A Congruence Criterion. Is he justified? Why or why not?
Ans: No, because the two triangles with equal corresponding angles need not be congruent. In such a corresponding one of them can be an enlarged copy of the other.

5). In the figure, the two triangles are congruent corresponding parts are marked.                              We can write ∆ RAT ≅ ?
Ans: From the given figure,
We may observe that,
∠ TRA = ∠ NWO      (given)
∠ TAR = ∠ NOW    (given)
∠ ATR = ∠ ONW    (given)
Hence, ∆ RAT ≅ ∆ WON

 

6. Complete the Congruence statement:


i) ∆ BCA = ?                      ii)  ∆ QRS = ?
Ans: i) Ans =∆ BTA                  ii) Ans = ∆ TPR


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

i) The triangles are congruent

Ans:
In the above figure, ΔABC and ΔDEF have equal areas.
And also, ΔABC ≅ ΔDEF
So, we can say that perimeters of ΔABC and ΔDEF are equal.
ii) The triangle are not congruent.

Ans:
In the above figure, ΔLMN and ΔOPQ
ΔLMN is not congruent to ΔOPQ
What can you say about their perimeters?
Ans: Since, ΔLMN is not congruent to ΔOPQ
So, we can also say that their perimeters are not same.

8). If ∆ ABC and ∆ PQR are to be congruent, name one additional pair of corresponding parts. What criterion did you use?
Ans:  By observing the figure, we can say that ∠ABC = ∠ PQR
∠ ACB = ∠ PRQ
The additional pair of corresponding part is BC = QR
∴ ∆ ABC ≅ ∆ PQR By A.S.A congruence criteria

9). Explain, why?
∆ ABC ≅ ∆ FED
Ans: From the figure, we find that
∠A = ∠ F
∠B = ∠E = 900
BC = ED
∴ ∆ ABC ≅ ∆ FED by A.S.A congruence criteria