Question

Please help me and explain :)

Answer 1

For the first question, we need two angles sitting on the line. We do not know if segments EG and AB are perpendicular, so cannot assume, even though they look like it.

A. DGB and EGA do not even have one leg common, so cannot be supplementary. so no.

B. DGB and CGB together add up to angle DGC which we know is a straight line. so yes.

C. CGB and AGD are vertical angles, and nothing tells us any of them is a right angle, so no.

D. EGA and EGC make an angle between segments CD and AB. so no.

E. EGD and CGB could be supplementary if we know CGB=EGC. But since we don't, so no.

For the second question, yes, you're right, take the second option in both, i.e. rotate 90 degrees (i.e. counterclockwise) about A, followed by a reflection about y, then translate downwards 20 units will give exactly GHIJ.

The fourth, rotate about B 90 degrees, then reflect about y-axis and translate down 25 is close, but need another translation (2,-1) to fit in the right place.