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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If 
are to be congruent, name one additional pair of corresponding parts. What criterion did you use?
In Fig. 6.57, state the three pairs of equal parts in ∆ABC and ∆EOD. Is ∆ABC ≅ ∆EOD? Why?
In Fig. 6.55, QS ⊥ PR, RT ⊥ PQ and QS = RT.
(i) Is ∆QSR ≅ ∆RTQ? Give reasons.
(ii) Is ∠PQR = ∠PRQ? Give reasons.
NCERT - Exemplar MathematicsIn each of the given pairs of triangles of Fig. 6.43, using only RHS congruence criterion, determine which pairs of triangles are congruent. In case of congruence, write the result in symbolic form:
Explain, why
