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Math Help - Need help with CONGRUENCY!!! @__@?

  1. #1
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    Cool Need help with CONGRUENCY!!! @__@?

    Please help me with this question (don't even know why it is related to congruency- pls answer in congruence method). Here goes:

    Given that a rhombus is a parallelogram with all sides equal, prove that its diagonals bisect each other at right angles.

    Thank you.
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  2. #2
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    I think you would start by proving the 4 triangles the diagonals create are all congruent.
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  3. #3
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    \overline{AD}\cong\overline{DC} Diagonols of parallegram bisect each other
    \overline{AB}\cong\overline{BC} Definition of Rhombus
    \overline{DB}\cong \overline{DB} Reflexive
    \triangle{ADB}\cong \triangle{CDB} SSS
    \angle{ADB}\cong \angle{CDB} Corresponding Parts of Congruent Triangles
    \angle{ADB}\cong \angle{CDB}=90^. Equal angles that form a linear pair must be 90
    \overline{BD}\perp \overline{AC} Lines that form 90 angles must be \perp
    Attached Thumbnails Attached Thumbnails Need help with CONGRUENCY!!! @__@?-rhombus.gif  
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