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.
2007-11-29 18:46:24 · 2 answers · asked by little zebulon 4 in Science & Mathematics ➔ Mathematics
How to prove they are right angles though?
2007-11-29 19:15:19 · update #1
Label the vertices A, B, C, and D, and label the intersection of the diagonals O. We have AD = AB because the sides of a rhombus are equal. We have DO = BO because the diagonals of a parallelogram bisect each other. Finally, AO = AO. Therefore, triangle AOD is congruent to triangle AOB. Hence, angle AOD = angle AOB; but the are supplements, so they must be 90 degrees.
2007-11-30 00:47:00 · answer #1 · answered by Tony 7 · 0⤊ 0⤋
the sides are equal , that means that they are congruent
maybe you can use that theparallelograms intersect the diagonals on their middle
and then use that in an insosceles traingle the median( that is the segment that splits the base into equal sides) is perpendicular to the base. That is the median is a perpendicular bisector. To prove this you may need the congruence method.
2007-11-29 19:04:29 · answer #2 · answered by Theta40 7 · 0⤊ 0⤋