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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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:

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Explain, why

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