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

Solution:

Given, the figure represents a triangle PQR.

QS ⊥ PR and RT ⊥ PQ

QS = RT

We have to determine if the triangles QSR and RTQ are congruent or not.

Considering the triangles QSR and RTQ,

Given, QS = RT

∠QSR = ∠QTR = 90°

Common side = QR

RHS congruence theorem states that, if the hypotenuse and side of one right-angled triangle are equal to the hypotenuse and the corresponding side of another right-angled triangle, the two triangles are congruent.

By RHS criterion, ∆QSR ≅ ∆RTQ

Corresponding parts of congruent triangles or cpct tell us that corresponding sides and corresponding angles of the two triangles which are congruent are equal.

By CPCT,

∠PQR = ∠PRQ

✦ Try This: In Fig, is the pair of triangles are congruent?

☛ Also Check: NCERT Solutions for Class 7 Maths Chapter 6

NCERT Exemplar Class 7 Maths Chapter 6 Problem 154

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

Summary:

In Fig. 6.55, QS ⊥ PR, RT ⊥ PQ and QS = RT. (i) ∆QSR ≅ ∆RTQ by RHS congruence criterion, (ii) ∠PQR = ∠PRQ by CPCT

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