Question

Lin knows that angle A is congruent to angle D. She claims that triangles ABC and DEF must be similar. Convince Lin that the triangles are not similar.

Answer 1

In order to determine similarity between two triangles, you need at least 2 angles to be congruent. If only 1 angle is congruent, the triangles are not similar. This is true because if 2 of the angles are congruent, then the remaining angle must be congruent also.

E.g. ∠A and ∠D both equal 90°, but ∠B and ∠C = 45°. While, ∠E = 30° and ∠F = 60°.