Q. 148

# In Fig. 6.50, which pairs of triangles are congruent by SAS congruence criterion (condition)? If congruent, write the congruence of the two triangles in symbolic form.

Answer :

(i) QR = SU

QP = TU

∠Q = ∠U

Hence; both triangles are congruent by SAS criterion

Δ PQR ≅ Δ TUS

(ii) JK = MN

JL≠NO

∠J = ∠N

Hence; both triangles are not congruent by SAS criterion

(iii) AB = BC

AE = CD

∠A = ∠C

Hence; both triangles are congruent by SAS criterion

Δ EAB ≅ Δ DCB

(iv) TS = XZ

TU = YZ

∠T = ∠Z

Hence; both triangles are congruent by SAS criterion

Δ STU ≅ Δ XZY

(v) OD = OH

OF = OC

∠FOD = ∠COH

Hence; both triangles are congruent by SAS criterion

Δ FOD ≅ Δ COH

(vi) AB = DE

AC≠DF

∠A = ∠D

Hence; both triangles are not congruent by SAS criterion

(vii) SP = QR

SQ = SQ

∠PSQ = ∠RQS

Hence; both triangles are congruent by SAS criterion

Δ PSQ ≅ Δ RQS

(viii) LM = OM

MN = MN

∠LMN = ∠OMN

Hence; both triangles are congruent by SAS criterion

Δ LMN ≅ Δ OMN

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Complete the congruence statement:

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NCERT MathematicsIn the figure, the two triangles are congruent. The corresponding parts are marked. We can write ?

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Triangles DEF and LMN are both isosceles with DE = DF and LM = LN, respectively. If DE = LM and EF = MN, then, are the two triangles congruent? Which condition do you use?

If ∠E = 40°, what is the measure of ∠N?

NCERT - Exemplar MathematicsIn Fig. 6.53, ∠1 = ∠2 and ∠3 = ∠4.

(i) Is ∆ADC ≅ ∆ABC? Why?

(ii) Show that AD = AB and CD = CB.

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In Fig. 6.52, DE = IH, EG = FI and ∠E = ∠I. Is ∆DEF ≅ ∆HIG? If yes, by which congruence criterion?

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In Fig. 6.51, PQ = PS and ∠1 = ∠2.

(i) Is ∆PQR ≅ ∆PSR? Give reasons.

(ii) Is QR = SR? Give reasons.

NCERT - Exemplar MathematicsIn Fig. 6.50, which pairs of triangles are congruent by SAS congruence criterion (condition)? If congruent, write the congruence of the two triangles in symbolic form.

NCERT - Exemplar Mathematics