On a card-sheet, draw a triangle of sides 4 cm, 3 cm and 2 cm. Cut it out. Make 13 more copies of the triangle and cut them out from the card sheet. Note that all these triangular pieces are congruent. Arrange them as shown in the following figure and make three triangles out of them.
Number of triangle: 1
Number of triangles: 4
Number of triangles: 9
∆ABC and ∆DEF are similar in the correspondence ABC ↔ DEF.
∠A ≅ ∠D, ∠B ≅ ∠E, ∠C ≅ ∠F and
AB/DE = 4/8 = 1/2; BC/EF = 3/6 = 1/2; AC/DF = 2/4 = 1/2 ... the corresponding sides are in proportion.
Similarly, consider ∆DEF and ∆PQR. Are their angles congruent and sides proportional in the correspondence DEF ↔ PQR?
