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Thread: 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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    $\displaystyle \overline{AD}\cong\overline{DC}$ Diagonols of parallegram bisect each other
    $\displaystyle \overline{AB}\cong\overline{BC}$ Definition of Rhombus
    $\displaystyle \overline{DB}\cong \overline{DB}$ Reflexive
    $\displaystyle \triangle{ADB}\cong \triangle{CDB}$ SSS
    $\displaystyle \angle{ADB}\cong \angle{CDB}$ Corresponding Parts of Congruent Triangles
    $\displaystyle \angle{ADB}\cong \angle{CDB}=90^.$ Equal angles that form a linear pair must be 90
    $\displaystyle \overline{BD}\perp \overline{AC}$ Lines that form 90 angles must be $\displaystyle \perp$
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