Question

Observe the following figures and state the test by which the triangles in each pair are congruent​

Answer 1

The test by which the triangles in given pairs are congruent​ is given below:

i) AB = PQ, BC = QR, and AC = PR

⇒ By SSS test

∆ABC ≅ ∆PQR

ii) XY = LM, YZ = MN and ∠XYZ = ∠LMN

⇒ By SAS test

∆ XYZ ≅ ∆LMN

iii) ∠ RPQ = ∠ TSU, ∠ PRQ = ∠STU, and the side between the equal angles (PR and SU) are also equal

⇒ By ASA test

∆PRQ ≅ ∆STU

iv) ∠ LMN = ∠ PTR = 90°, Hypotenuse LN = Hypotenuse PR, and side LM = side PT

⇒ By RHS test

∆LMN ≅ ∆PTR

(The figures from the question are attached below.)