Triangles

In triangle ABC, if DE is parallel to BC where D and E are points on AB and AC respectively, and AD = 4 cm, DB = 6 cm, AE = 3 cm, then find EC.

Two triangles ABC and PQR are similar. If AB = 6 cm, BC = 8 cm, AC = 10 cm and PQ = 9 cm, then find QR.

In triangle PQR, if angle P = 60°, angle Q = 80°, and in triangle XYZ, angle X = 60°, angle Y = 80°, then which similarity criterion proves that triangle PQR ~ triangle XYZ?

If triangle ABC ~ triangle DEF with ratio of similarity 2:3, and area of triangle ABC is 16 cm², then find the area of triangle DEF.