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

Expert Answer:

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