A point O is taken inside an equilateral four sided figure ABCD such that its distances from the angular points D and B are equal. Show that AO and OC are in one and the same straight line.
Asked by Topperlearning User | 10th Aug, 2017, 12:36: PM
In AOD and AOB
AD = AB (given)
AO =AO (common side)
OD = OB (given)
AOD AOB (SSS congruence rule)
AOD = AOB (c.p.c.t)
Similarly, DOC BOC (SSS congruence rule)
DOC = BOC (c.p.c.t)
AOD + AOB + DOC + BOC = 360o (angles at a point)
2AOD + 2DOC = 360o
AOD + DOC = 180o
Hence, AO and OC are in one and the same straight line.
Answered by | 10th Aug, 2017, 02:36: PM
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