# Thread: Need help with CONGRUENCY!!! @__@?

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

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

Thank you.

2. I think you would start by proving the 4 triangles the diagonals create are all congruent.

3. $\overline{AD}\cong\overline{DC}$ 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 $\perp$