Question

State which pair of triangles in the following figure are similar. Write the similarity criterion used by you for answering the question, and also write the pairs of similar triangles in the symbolic form:

Answer 1

In ΔDEF,

∠D + ∠E + ∠F = 180°

(Sum of the measures of the angles of a triangle is 180°.)

70° + 80° +∠F = 180°

∠F = 30°

Similarly, in ΔPQR,

∠P + ∠Q + ∠R = 180°

(Sum of the measures of the angles of a triangle is 180°.)

∠P + 80° + 30° = 180°

∠P = 70°

In ΔDEF and ΔPQR,

∠D = ∠P     ...(Each 70°)

∠E = ∠Q     ...(Each 80°)

∠F = ∠R      ...(Each 30°)

∴ ΔDEF ∼ ΔPQR       ...[By AAA similarity criterion]