Maths!!!
Please can anyone help with this?? I'm stuck...
Find an expression for the length of the line segment EF in terms of a and b.
Find an expression for the length of the line segment EF in terms of a and b.
(edited 1 year ago)
Reply 1
21
What can you say about the three triangles inside the parallelogram with a vertex where AD and CB intersect, so with bases AB, CD, EF?
Reply 2
19
Similar? I haven't been thinking about angles but now it looks better
Reply 3
21
Original post by Bookworm524
Similar? I haven't been thinking about angles but now it looks better
Yes theyre similar. Its the famous/old Thales theorem. So the heights are in the ratio of the bases which should get you there.
Reply 4
19
I guessed (a-b)/2 and somehow this is correct?!
Reply 5
19
But I don't actually know how to get there
Reply 6
21
Original post by Bookworm524
But I don't actually know how to get there
Draw the similar triangles and think how the bases/heights are related.
Reply 7
Original post by mqb2766
Yes theyre similar. Its the famous/old Thales theorem. So the heights are in the ratio of the bases which should get you there.
but we don't know the heights??
Reply 8
21
Original post by iwantoknowhy
but we don't know the heights??
As in the post you quoted, the heights ratio are the same ratio of the bases as theyre similar.
Reply 9
Original post by mqb2766
As in the post you quoted, the heights ratio are the same ratio of the bases as theyre similar.
It's the length of the base we're trying to work out so we don't know the ratio of the bases either? I thought you were saying to use the ratio of the heights to work out the ratio of the bases but clearly I'm more confused than I thought 😭
(edited 9 months ago)
Reply 10
21
Original post by iwantoknowhy
It's the length of the base we're trying to work out so we don't know the ratio of the bases either? I thought you were saying to use the ratio of the heights to work out the ratio of the bases but clearly I'm more confused than I thought 😭
You know the ratio of AB to CD and you know E and F are at the midpoints of the diagonals.
Reply 11
Original post by mqb2766
You know the ratio of AB to CD and you know E and F are at the midpoints of the diagonals.
You do...
I feel like I'm missing something obvious here but I can't see how that's helpful 😭
Thank you for all your help and patience!
Reply 12
21
Original post by iwantoknowhy
You do...
I feel like I'm missing something obvious here but I can't see how that's helpful 😭
Thank you for all your help and patience!
I feel like I'm missing something obvious here but I can't see how that's helpful 😭
Thank you for all your help and patience!
Sometimes it worth doing a simple example with numbers, then redo it with algebra to get the general solution.
So if a=2, b=1 and h=1, can you work out what EF is? Obviously, if a=b, the EF is zero as the diagonals will cross at the midpoint.
Labelling the diagonal crossing point G, consider
ABG and CDG, then
CDG and EFG
(edited 9 months ago)
Reply 13
Ohhh I get it now thank you so much!
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