Q. 1545.0( 2 Votes )

In Fig. 6.55, QS PR, RT PQ and QS = RT.



(i) Is ∆QSR ∆RTQ? Give reasons.

(ii) Is PQR = PRQ? Give reasons.

Answer :

Given: QS PR, RT PQ and QS = RT


Formula Used/Theory:-


If hypotenuse and 1 sides of Right angled triangle are equal in both the triangles then both triangles are congruent by RHS congruence criterion


In ∆QSR and ∆RTQ


As ∆QSR, ∆RTQ both are right angle triangle


Right angled at QSR and RTQ


QR = QR (Hypotenuse)


QS = TR (Given)


∆QSR ∆RTQ


Hence; both triangles are congruent by RHS criterion


If ∆QSR ∆RTQ then;


All 3 angles of one triangle will be equal to all 3 angles of another triangles


⇒ ∠Q = R


QTR = QSR


SQR = QRT


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