Me asap sos!
in the figure below, ∠abc ≅ ∠dec and ∠gfe ≅ ∠dce. point c is the point of intersection between segment ag and segment bd, while point e is the point of intersection between segment ag and segment df.
prove δabc ~ δgef. in paragraph form!

If we're trying to prove similarity, it's only sufficient to prove two angles are equal, because by def, the third angle must be equal.

in  δabc and  δgef,
∠abc =  ∠dec (given)
but,  ∠dec =  ∠feg (vertically opposite angles)
∴  ∠abc =  ∠feg

similarly,  ∠gfe =  ∠dce (given)
but,  ∠dce =  ∠bca (vertically opposite angles are equal)
∴  ∠gfe =  ∠bca

since two angles are equal, by definition, the third angle must be equal, and hence, we've proved the two triangles are similar as they are equi-angular.