Step 1

The lines VW and GF are parallel.

And the rest two lines act as traversals

Step 2

\(\displaystyle\angle{G}{E}{F}\stackrel{\sim}{=}\angle{W}{E}{V}\) (Vertically opposite angles)

\(\displaystyle\angle{E}{F}{G}\stackrel{\sim}{=}\angle{E}{V}{W}\) (Alternate interior angles because \(\displaystyle{F}{G}{p}{a}{r}{a}{l}\le{l}{W}{V}\))

\(\displaystyle\angle{F}{G}{E}\stackrel{\sim}{=}{V}{W}{E}\) (Alternate interior angles)

Hence by AAA criterion

\(\displaystyle\triangle{E}{F}{G}\sim{E}{V}{W}\)

The lines VW and GF are parallel.

And the rest two lines act as traversals

Step 2

\(\displaystyle\angle{G}{E}{F}\stackrel{\sim}{=}\angle{W}{E}{V}\) (Vertically opposite angles)

\(\displaystyle\angle{E}{F}{G}\stackrel{\sim}{=}\angle{E}{V}{W}\) (Alternate interior angles because \(\displaystyle{F}{G}{p}{a}{r}{a}{l}\le{l}{W}{V}\))

\(\displaystyle\angle{F}{G}{E}\stackrel{\sim}{=}{V}{W}{E}\) (Alternate interior angles)

Hence by AAA criterion

\(\displaystyle\triangle{E}{F}{G}\sim{E}{V}{W}\)