Distance AB = √((5-2)² + (7-3)²) = √(3² + 4²) = √(9 + 16) = √25 = 5.

The ratio of the longest sides is 10 cm to 5 cm, which simplifies to 2:1. Therefore, the sides of triangle JKL are in the ratio 2:1.

Distance = √((4-1)² + (6-2)²) = √(3² + 4²) = √(9 + 16) = √25 = 5.

Using the Pythagorean theorem, 12² + 16² = 144 + 256 = 400 = 20², so triangle MNO is a right triangle.

The sides of triangle PQR are in the ratio 12:16:20 = 3:4:5, which matches triangle ABC, confirming similarity.