so here we have a question where they've given us a few things they've told us that the length of a b is 20 they've also told us that by showing us these lines they're telling us that d is the midpoint of that shape then they tell us that ae is equal to six so it's all stuff that you can pretty much see on the diagram okay now the point is we need to work out the value of y and so y is over here so if we had to zone in onto this triangle here we would see the following we see that we've got a midpoint can you see d is the midpoint because they've showed us with this and this and then they've told us that these two lines are parallel now remember when that happens in a triangle it automatically means that it cuts the opposite side so ae and ec in half that means that ec is also going to be equal to 6 but now the reason is going to be converse because remember that's not the original midpoint theorem the original midpoint theorem is if you have two midpoints so that's going to be converse midpoint theorem or your teacher might say line through midpoint parallel to other side so it's the line going through d which is a midpoint and that line is parallel so these two so it's parallel to the other side okay so ec is going to be 6 and that means y is equal to 6. the next question asks us to work out the value of x and we must just remember that ae is now going to be equal to ec so inside this triangle over or inside triangle abc we now have this midpoint over here as well so the next one is to work out the value of x which is over here so if we had to zone into this triangle we can then say that af is equal to 8 because why do we say that well in that triangle we've got a midpoint over there because we discovered that in the previous question and these two sides are parallel and so when that happens we can say that it's going to cut the opposite side exactly in half so we can say that this side is going to be the exact same as that side over there but that's not the original midpoint theorem because remember the original midpoint theorem is when you have the two midpoints already but here we had the midpoint and a parallel line so what we'll say is converse midpoint theorem or remember your teacher might say line through midpoint parallel to other side and that's it