anonymous
  • anonymous
ABC and DBC are two triangles on the same base BC such that A and D lie on the opposite sides of BC, AB = AC and DB = DC. Show that AD is the perpendicular bisector of BC.
Mathematics
jamiebookeater
  • jamiebookeater
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anonymous
  • anonymous
|dw:1344485886935:dw|
anonymous
  • anonymous
|dw:1344486523841:dw|
anonymous
  • anonymous
ok

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anonymous
  • anonymous
1...show that triangle ABD=triangle ACD......it gives BE=EC 1...show that triangle ABE=triangle AEC......it gives
anonymous
  • anonymous
I have shown that triangle ABD = ACD, but I don't know how to do the other one.
anonymous
  • anonymous
triangle ABE=triangle AEC because 1...AC=AB 2...BE=EC 3...AE=AE
anonymous
  • anonymous
But we have to prove that BE = EC right?
anonymous
  • anonymous
Perpendicular bisector.
anonymous
  • anonymous
u've shown that triangle ABD=triangle ACD am i right?
anonymous
  • anonymous
yes.
anonymous
  • anonymous
sorry if I take a little long to reply.
anonymous
  • anonymous
np....:)
anonymous
  • anonymous
well it gives BE = EC
anonymous
  • anonymous
But how?
anonymous
  • anonymous
I mean, its not a side of ABD or ACD.
anonymous
  • anonymous
u r right ... thats not a complete proof... lets think again...
anonymous
  • anonymous
we need to show that triangle ABE=triangle AEC...........
anonymous
  • anonymous
try to find 2 angles equal...and one side equal for that 2 triangle
anonymous
  • anonymous
AB = AC
anonymous
  • anonymous
|dw:1344488387156:dw|
anonymous
  • anonymous
so that you don't need to scroll up too much.
anonymous
  • anonymous
lol.........:)
anonymous
  • anonymous
we proved that triangle ABD=triangle ACD so that...
anonymous
  • anonymous
AE is common so triangle AEB = AEC.
anonymous
  • anonymous
we are done
anonymous
  • anonymous
But how does that prove that AD is the perpendicular bisector?
anonymous
  • anonymous
We should prove that AD bisects BC and angle AEB = 90 degrees.
anonymous
  • anonymous
it provides BE=EC and
anonymous
  • anonymous
Thanks a lot mukushla!!!
anonymous
  • anonymous
yw......:)

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