CBSE Class 9 Answered
Show that the diagonals of a rhombus are
perpendicular to each other.
Asked by Topperlearning User | 04 Jun, 2014, 01:23: PM
Expert Answer
Given:
ABCD is a rhombus. Diagonal AC and BD intersect at O.
To prove:
AC and BD bisect each other at right angles.
Proof:
A rhombus is a parallelogram such that,
AB = DC = AD = BC ---(i)
Also, the diagonals of a parallelogram bisect each other.
Hence, BO = DO and AO = OC ---(ii)
Now, compare AOB and AOD,
AB = AD (from (i) above)
BO = DO (from (ii) above)
AO = AO (common side)
Therefore, AOB AOD (SSS Congruency Condition)
Therefore, AOB = AOD (corresponding parts)
BD is a straight line segment.
Therefore, AOB + AOD = 1800
But, AOB = AOD (Proved)
AOB = AOD = 1800/ 2 = 900
i.e., the diagonals are perpendicular to each other.
Answered by | 04 Jun, 2014, 03:23: PM
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