By which congruence criterion, the two triangles in Fig. 6.19 are congruent?
(a) RHS
(b) ASA
(c) SSS
(d) SAS

Solution:

Given, the figure represents two triangles PQR and PQS.

We have to find the type of congruence criterion.

Considering triangles PQR and PQS,

PR = PS = a cm

RQ = SQ = b cm

Common side = PQ

Side-Side-Side congruence rule states that if three sides of one triangle are equal to three corresponding sides of another triangle, then the triangles are congruent.

By SSS rule, ΔPQR ≅ ΔPQS

Therefore, the required congruence criterion is SSS.

✦ Try This: In a triangle ABC, ∠A - ∠B = 30° and ∠A - ∠C = 42°; find angle A

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

NCERT Exemplar Class 7 Maths Chapter 6 Problem 46

By which congruence criterion, the two triangles in Fig. 6.19 are congruent? (a) RHS, (b) ASA, (c) SSS, (d) SAS

Summary:

The two triangles are congruent by SSS congruence criterion.

☛ Related Questions:

• By which of the following criteria two triangles cannot be proved congruent? (a) AAA, (b) SSS, (c) S . . . .
• If ∆PQR is congruent to ∆STU (Fig. 6.20), then what is the length of TU? (a) 5 cm, (b) 6 cm, (c) 7 c . . . .
• If ∆ABC and ∆DBC are on the same base BC, AB = DC and AC = DB (Fig. 6.21), then which of the followi . . . .