Chapter 7 Congruence of Triangles 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
Answer: ∆ABC ≅ ∆DEF (by SSS rule)
(b) Given: ZX = RP
RQ = ZY
∠PRQ = ∠XZY
So, ΔPQR ≅ ΔXYZ
Answer: ∆PQR ≅ ∆XYZ (BY SAS rule)
(c) Given: ∠MLN = ∠FGH
∠NML = ∠GFH
∠ML = ∠FG
So, ΔLMN ≅ ΔGFH
Answer: ∆LMN ≅ ∆GFH (BY ASA rule)
(d) Given: EB = DB
AE = BC
∠A = ∠C = 90°
So, ΔABE ≅ ΔACD
Answer: ∆ABE ≅ ∆CDB (BY RHS rule)
Question 2: You want to show that ΔART ≅ ΔPEN,
(a) If you have to use SSS criterion, then you need to show
(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 = EN
(ii) PN = AT
(c) If it is given that AT = PN and you are to use ASA criterion, you need to have
(i) and (ii)
Answer:
(i) ∠ATR = ∠PNE
(ii) ∠RAT = ∠EPN
Question 3: You have to show that ΔAMP ≅ ΔAMQ.
In the following proof, supply the missing reasons.
Steps |
Reasons |
(i) PM = QM |
(i) … |
(ii) ∠PMA = ∠QMA |
(ii) … |
(iii) AM = AM |
(iii) … |
(iv) ΔAMP ≅ ΔAMQ |
(iv) … |
Answer:
Steps |
Reasons |
(i) PM = QM |
from the given figure |
(ii) ∠PMA = ∠QMA |
from the given figure |
(iii) AM = AM |
common side for the both triangles |
(iv) ΔAMP ≅ ΔAMQ |
(by SAS congruence property) |
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: The student is not justified because AAA congruence criterion do not exist.
Question 5: In the figure, the two triangles are congruent. The corresponding parts are marked. We can write ΔRAT ≅ ?
Answer:
Question 6: Complete the congruence statement:
ΔBCA ≅ ΔQRS ≅
Answer:
Question 7: In a squared sheet, draw two triangles of equal areas such that
(i) The triangles are congruent.
Answer:
⃤ ABC and ⃤ MNO have the same length. So the area of these triangles is the same.
(ii) The triangles are not congruent.
What can you say about their perimeters?
Answer:
⃤ ABC and ⃤ PQR do not have the same length. So the area of these triangles is not the 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:
Question 9: If ΔABC and ΔPQR are to be congruent, name one additional pair of corresponding parts. What criterion did you use?
Answer:
Question 10: Explain, why ΔABC ≅ ΔFED
Answer:
In ∆ABC and ∆FED
∠B = ∠E = 90° (given)
∠A = ∠F (given)
Therefore, ∠A + ∠B = ∠E + ∠F
180° – ∠C = 180° – ∠D
(by Angle sum property)
Therefore, ∠C =∠D
BC = ED (given)
Therefore, ∆ABC = ∆FED (by ASA Congruence Criterion)
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