O is the point inside a rhombus ABCD such that BO = OC prove that AO and OC - Maths - Quadrilaterals

Question

O is the point inside a rhombus ABCD such that BO = OC prove
that AO and OC are in same straight line

Priyanka Kedia · Accepted Answer

Recheck your given part, there should be BO=OD instead of BO=OC

$L e t A B C D i s a r hom b u s a n d p o int O i s i n s i d e i t s u c h t h a t B O = O D T o P r o v e : A O a n d O C a r e i n t h e s a m e s t r a i g h t l i n e P r o o f : I n Δ A O D a n d Δ A O B, A D = A B (S i d e s o f a r hom b u s a r e e q u a l) A O = A O (c o m m o n) B O = O D (g i v e n) \Rightarrow Δ A O D ≅ Δ A O B (b y S S S c r i t e r i o n o f c o n g r u e n c e) \Rightarrow ∠ B O A = ∠ A O D S i m i l a r l y, ∠ B O C = ∠ C O D B u t, ∠ B O A + ∠ A O D + ∠ B O C + ∠ C O D = 360^{0} \Rightarrow 2 ∠ A O D + 2 ∠ C O D = 360^{0} \Rightarrow ∠ A O D + ∠ C O D = 180^{0} \Rightarrow A O a n d O C a r e i n t h e s a m e s t r a i g h t l i n e H e n c e p r o v e d$

O is the point inside a rhombus ABCD such that BO = OC . prove that AO and OC are in same straight line