Question

Δ PQR and Δ TQR are on the same base QR and on the same side of QR. If PQ = TR and PR = TQ; then which of the following is correct ?
1. Δ PQR ≅ Δ TQR
2. Δ PQR ≅ Δ TRQ
3. Δ PQR ≅ Δ RQT
4. Δ PQR ≅ Δ QTR

Answer 1

Correct Answer - Option 2 : Δ PQR ≅ Δ TRQ

Given:

PQ = TR 

PR = TQ

Concept used:

SSS congruence rule → If all three sides of one triangle are equal to the corresponding sides of another triangle, then the two triangles are congruent

Detailed solution:

Comparing the equal sides of the two triangles,

PQ = TR

PR = TQ

QR = QR

∴ Δ PQR ≅ Δ TRQ