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

(i) Is ∆QSR ≅ ∆RTQ? Give reasons.

(ii) Is ∠PQR = ∠PRQ? Give reasons.

Question

In Fig. 6.55, QS ⊥ PR, RT ⊥ PQ and QS = RT. (i) Is ∆QSR ≅ ∆RTQ? Give reasons. (ii) Is ∠ PQR = ∠ PRQ? Give reasons.

Philoid · Accepted 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

In Fig. 6.55, QS ⊥ PR, RT ⊥ PQ and QS = RT.(i) Is ∆QSR ≅ ∆RTQ? Give reasons.(ii) Is ∠PQR = ∠PRQ? Give reasons.