Answer it plz for 10points
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Step-by-step explanation:
Given : Point O is taken inside a rhombus ABCD such that BO = OD.
To prove : AO and OC are in one and the same St. line.
Proof : In ∆s AOD and AOB, we have
AD = AB (given)
AO = AO
OD = OB (given)
∴ ∆ AOD ≌ ∆AOB (SSS axiom of congruence)
∴ ∠1 = ∠2 (cpct)
similarly, ∆DOC ≌ ∆BOC
∴ ∠3 = ∠4
But ∠1 + ∠2 + ∠3 + ∠4 = 360° (∠s round a point)
or 2∠2 + 2∠3 = 360° ( ∵ ∠1 = ∠3 and ∠3 = ∠ 4)
⇛ ∠2 + ∠3 = 180° (proved above)
Therefore, their outer arms AO and BO are in one and the same St. line. (Axiom of linear pair)
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