Q149 of 158 Page 159

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

PQ = ST


QR = TU


∠Q = ∠T


Hence; both triangles are congruent by SAS criterion


Δ PQR ≅ Δ STU


(b) AB = XZ


∠A = ∠X


YZ≠BC (Hypotenuse )


AC≠XY


Hence; both triangles are not congruent neither by RHS nor by


SAS congruence criterion


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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?

 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.




 150

In Fig. 6.51, PQ = PS and ∠1 = ∠2.


(i) Is ∆PQR ≅ ∆PSR? Give reasons.


(ii) Is QR = SR? Give reasons.

 151

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