1. A line is perpendicular to a plane, if and only if, the line
intersects the plane in a point and is perpendicular to
every line in the plane that intersects it at that point.

2. line
points
one point
noncollinear
noncollinear
lies in the plane
line

3. 8
noncollinear

4. Q
V, Y and W
line b

5. Postulate 7 allows me to say the intersection between two lines is a point.
Postulate 5: Points X and Y create a line called line a.
Postulate 6: Line a contains points X and Y.

6. coplanar
∠BHD
∠BHD
collinear H

7. between
perpendicular

8. T
BD EC T
EC plane G

9. The diagram would change by adding congruence symbols on segments RX and XS and point X would be the midpoint of segment RS.
Yes, you can CONCLUDE that BD is the intersection of plane F and plane G because it's the line that's formed when the two planes intersect.