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pratu043

  • 3 years ago

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.

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  1. pratu043
    • 3 years ago
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    |dw:1344485886935:dw|

  2. mukushla
    • 3 years ago
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    |dw:1344486523841:dw|

  3. pratu043
    • 3 years ago
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    ok

  4. mukushla
    • 3 years ago
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    1...show that triangle ABD=triangle ACD......it gives BE=EC 1...show that triangle ABE=triangle AEC......it gives <AEB=<AEC=90

  5. pratu043
    • 3 years ago
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    I have shown that triangle ABD = ACD, but I don't know how to do the other one.

  6. mukushla
    • 3 years ago
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    triangle ABE=triangle AEC because 1...AC=AB 2...BE=EC 3...AE=AE

  7. pratu043
    • 3 years ago
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    But we have to prove that BE = EC right?

  8. pratu043
    • 3 years ago
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    Perpendicular bisector.

  9. mukushla
    • 3 years ago
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    u've shown that triangle ABD=triangle ACD am i right?

  10. pratu043
    • 3 years ago
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    yes.

  11. pratu043
    • 3 years ago
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    sorry if I take a little long to reply.

  12. mukushla
    • 3 years ago
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    np....:)

  13. mukushla
    • 3 years ago
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    well it gives BE = EC

  14. pratu043
    • 3 years ago
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    But how?

  15. pratu043
    • 3 years ago
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    I mean, its not a side of ABD or ACD.

  16. mukushla
    • 3 years ago
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    u r right ... thats not a complete proof... lets think again...

  17. mukushla
    • 3 years ago
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    we need to show that triangle ABE=triangle AEC...........

  18. mukushla
    • 3 years ago
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    try to find 2 angles equal...and one side equal for that 2 triangle

  19. pratu043
    • 3 years ago
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    AB = AC

  20. pratu043
    • 3 years ago
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    |dw:1344488387156:dw|

  21. pratu043
    • 3 years ago
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    so that you don't need to scroll up too much.

  22. mukushla
    • 3 years ago
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    lol.........:)

  23. mukushla
    • 3 years ago
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    we proved that triangle ABD=triangle ACD so that... <BAE=<CAE and what is the third condition?

  24. pratu043
    • 3 years ago
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    AE is common so triangle AEB = AEC.

  25. mukushla
    • 3 years ago
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    we are done

  26. pratu043
    • 3 years ago
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    But how does that prove that AD is the perpendicular bisector?

  27. pratu043
    • 3 years ago
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    We should prove that AD bisects BC and angle AEB = 90 degrees.

  28. mukushla
    • 3 years ago
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    it provides BE=EC and <AEB=<AEC but we know that <AEB+<AEC=180

  29. pratu043
    • 3 years ago
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    Thanks a lot mukushla!!!

  30. mukushla
    • 3 years ago
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    yw......:)

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