Question

In the given figure, a point O is taken inside an equilateral quadrilateral ABCD such that OB =OD. Show that A, O and are in the same straight line.​

Answer 1

SOLUTIONS:

Given: A quadrilateral ABCD in which AB = BC = CD = DA and O is a point within it such that OB = OD.

To prove: ∠AOB +∠COB = 180°.

Proof: In △OAB and △OAD, we have

AB = AD [Given]

OA = OA [Common]

OB = OD [Given]

∴ △OAB ≅△OAD

∴ ∠AOB = ∠AOD .....(i)[c.p.c.t.]

Similarly, △OBC ≅ △ODC.

∴ ∠COB = ∠COD .....(ii)

Now,

∠AOB +∠COB +∠COD +∠AOD = 360° [Angles at a point]

→2(∠AOB +∠COB) = 360°

→∠AOB +∠COB = 180°