Iam trying to finish geometry over the summer.

Great.  If you like it there's more geometry to learn than you can in one lifetime, so you're never finished.

Anyway, this is the 30/60/90 right triangle, which you'll soon learn is the biggest cliche in trigonometry.  It's a pretty basic object, being half an equilateral triangle.  So if the hypotenuse is  the small side is  and the middle side  (which would be an altitude of the equilateral triangle). We write the Pythagorean Theorem:









So the sides opposite 30/60/90 respectively are in the ratio of  or equivalently  .

We have E=30, F=60, G=90, with respective opposite sides FG:EG:EF in ratio .   From the ratios we get



A.  TRUE

B. FALSE, 

C. FALSE, 

D. TRUE (see above)

E. TRUE (see above)

F. FALSE (see above)

That looks good.