Q148 of 158 Page 159

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.




(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


More from this chapter

All 158 →
146

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?

 147

If ∆PQR and ∆SQR are both isosceles triangle on a common base QR such that P and S lie on the same side of QR. Are triangles PSQ and PSR congruent? Which condition do you use?

 149

State which of the following pairs of triangles are congruent. If yes, write them in symbolic form (you may draw a rough figure).

A. ∆PQR : PQ = 3.5 cm, QR = 4.0 cm, ∠Q = 60°


∆STU : ST = 3.5 cm, TU = 4 cm, ∠T = 60°


B. ∆ABC : AB = 4.8 cm, A = 90°, AC = 6.8 cm


∆XYZ : YZ = 6.8 cm, ∠X = 90°, ZX = 4.8 cm

 150

In Fig. 6.51, PQ = PS and ∠1 = ∠2.


(i) Is ∆PQR ≅ ∆PSR? Give reasons.


(ii) Is QR = SR? Give reasons.