Which congruence criterion do you use in the following? (a) Given: AC = DF, AB = DE, BC = EF So If ∆ ABC ≅ ∆ DEF (b) Given: RP = ZX, RQ = ZY, ∠PRQ = ∠XZY So ∆ PQR ≅ ∆ XYZ (c) Given: ∠MLN = ∠FGH, ∠NML = ∠HFG, ML = FG So ∆LMN ≅ ∆GFH (d) Given: EB = BD, AE = CB, ∠A = ∠C = 90° So ∆ABE ≅ ∆CDB

(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, ∆ABC ≅ ∆DEF

(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, ∠PRQ ≅ ∠XyY

(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, ∆LMN ≅ ∆GFH

(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, ∆ABE ≅ ∆CDB

Class 7 Maths Chapter 7 Exercise 7.2

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