Question

In the given figure, ∠1 = ∠2 and `(AC)/(BD) = (CB)/(CE)`. Prove that ΔACB ~ ΔDCE.

Answer 1

We have : 

`(AC)/(BD)=(CB)/(CE)` 

⟹ `(AC)/(CB)=(CD)/(CE)` (𝑆𝑖𝑛𝑐𝑒,𝐵𝐷=𝐷𝐶 𝑎𝑠 ∠1= ∠2 )
Also, ∠1= ∠2
i.e, ∠𝐷𝐵𝐶=∠𝐴𝐶𝐵
Therefore, by SAS similarity theorem, we get :
Δ ACB - Δ DCE