Question

State which pair of triangles in the figure given below is similar. Write the similarity criterion used, and also write the pair of similar triangles in symbolic form.

Answer 1

⇒ For ΔABC,

∠B = 25°, ∠C = 30°

So,

∠A = 180° − (25° + 30°)

∴ ∠A = 125°

⇒ For ΔDEF,

∠D = 25°, ∠F = 125°

So,

∠E = 180° − (25° + 125°)

∴ ∠E = 30°

Now let’s compare the angles:

∠A = ∠F = 125°

∠B = ∠D = 25°

∠C = ∠E = 30°

Therefore, the triangles are similar by the AAA (Angle-Angle-Angle) similarity criterion.

The pair of similar triangles in symbolic form:

△ABC ∼ △FDE or equivalently, △BCA ∼ △DEF