The ratio of the areas of similar triangles is the square of the ratio of their corresponding sides. (4/8)² = 1/4.

The ratio of the lengths of corresponding sides of similar triangles is equal to the ratio of any two corresponding sides, which is 4:8 or 1:2.

Congruent triangles have corresponding angles that are equal.

In a 45-45-90 triangle, the sides opposite the 45-degree angles are equal, hence the ratio is 1:1.

In a 45-45-90 triangle, the sides opposite the 45-degree angles are equal, so HI = GH√2 = 5√2 cm.

The length of the diagonal can be found using the Pythagorean theorem: d = √(3² + 4²) = √(9 + 16) = √25 = 5 cm.