Congruence of Triangles

Exercise 7.2

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

congruent triangles

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

Answer: SSS criterion

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

congruent triangles

Answer: SAS Criterion


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

congruent triangles

Answer: ASA Criterion

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

congruent triangles

Answer: SAS Criterion

Question 2: You want to show that ΔART ≈ΔPEN

congruent triangles

(a) If you have to use SS criterion, then you need to show (i) AR = (ii) RT = (iii) AT =

Answer: (i) → PE, (ii) → EN (iii) → PN

(b) It is given that angle T = angle N and you are to use SAS criterion, you need to have (i) RT = and (ii) PN =

Answer: (i) → EN, (ii) → AT

(c) If it is given that AT = PN and you use ASA criterion, you need to have (i) ? (ii) ?

Answer: (i) ∠A = ∠P (ii) ∠T = ∠N

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

congruent triangles

Asnwer:

StepsReasons
(a) PM = QMEqual measure
(b) ∠PMA = ∠QMAEqual measure
(c) AM = AMEqual measure
(d) ΔAMP ≈ ΔAMQSAS criterion

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: AAA is not a criterion for congruence. Hence, the student is wrong. This can be understood by taking the example of equilateral triangles. Each angle of an equilateral triangle is 60°; no matter what is the size of the triangle. So, all equilateral triangle need not be congruent.

Question 5: In the figure, two triangles are congruent. The corresponding parts are marked. We can write ΔRAT ≈…………..

congruent triangles

Answer: ΔWON

Question 6: Complete the congruence statement: ΔBCA ≈ …………. ΔQRS ≈ ……………….

congruent triangles congruent triangles

Answer: ΔBCA ≈ ΔBTA and ΔQRS ≈ ΔQPT


Question 7: In a squared sheet, draw two triangles of equal areas such that
(a) The triangles are congruent.
(b) The triangles are not congruent.
What can you say about their perimeters?

Answer: When triangles are congruent then their perimeters are equal. But when triangles are not congruent then their perimeters are different.

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: Five pairs of congruent parts can be three pairs of sides and two pairs of angles. In that case, SAS or ASA criterion would prove them to be congruent. Hence, such a figure is not possible.

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

congruent triangles

Answer: : BC = QR; ASA criterion

Question 10: Explain, why: ΔABC ≈ ΔFED

congruent triangles

Answer: Angle B = angle E,
BC = ED
and angle F = angle A
Hence, as per ASA criterion, triangles are congruent.



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