In triangle ABC and DEF, ∠A = ∠D and $\dfrac{\text{AB}}{\text{AC}} = \dfrac{\text{DE}}{\text{DF}}$ then prove that Δ ABC ∼ Δ DEF.

In triangle ABC and DEF, ∠A = ∠D, ∠B = ∠E and ∠C = ∠F. Also, AL and DM are medians. Prove that $\dfrac{\text{BC}}{\text{EF}} = \dfrac{\text{AL}}{\text{DM}}$.

In the given figure, Δ ABC and Δ DEF are similar, BM and EN are their medians. If Δ ABC is similar to Δ DEF, prove that :

(i) Δ AMB ∼ Δ DNE

(ii) Δ CMB ∼ Δ FNE

(iii) $\dfrac{BM}{EN} = \dfrac{AC}{DF}$

In the given figure, Δ ABC is isosceles and AP x BQ = AC², prove that Δ ACP ∼ Δ BCQ.