Which congruence criterion do you use in the following?

(a) Given: AC=DF

AB=DF

BC=EF

∆ABC ∆DEF

(b) Given: ZX=R

RQ=ZY

∠PQR = ∠XYZ

∆PQR ∆XYZ

(c) ∠MLN = ∠FGH

∠NML = ∠GFH

ML=FG

∆LMN ∆GFH

(d) Given: EB=DB

AE=BC

∠A = ∠C=90^{o}

∆ABC ∆CDB

(a) In the above given question, we have given that:

AB = DE

Also, BC = EF

And, AC = DF

Therefore, both the triangles are equal by SSS congruence criterion

As, the sides of both the triangles are equal.

(b) In the above given question, we have given that:

ZX = RP

Also,

RQ = ZY

And,

∠PQR = ∠XYZ

Therefore, both the triangles are equal by SAS congruence criterion

As,

Two sides of both the triangles are equal. Also, ∠PQR and ∠XYZ are equal.

(c) In the above given question, we have given that:

∠MLN = ∠FGH

Also,

∠NML = ∠GFH

And,

ML = FG

Therefore, both the triangles are equal by SAS congruence criterion

As, two angles and the side included between these angles of ∠LMN are equal to two angles and the side included between these angles of ∠GFH.

(d) In the above given question, we have given that:

EB = DB

Also,

AE = BC

And,

∠A = ∠C = 90^{o}

Therefore, both the triangles are equal by RHS congruence criterion

As, two right triangles, one side and hypotenuse of the above given triangles are equal

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