Answer:
OM = ON by using concurrency of Δs BOM and DON
Step-by-step explanation:
In the figure ABCD:
∵ AB // CD
∵ CB // AD
∵ In any quadrilateral If every two sides are parallel then
it will be a parallelogram
∴ ABCD is a parallelogram
∴ AC and BD bisects each other at O ⇒ (properties of parallelogram)
∴ OD = OB ⇒ (1)
∵ BC // AD
∴ m∠CBD = m∠ADB ⇒ alternate angles
∵ M ∈ BC , N ∈ AD , O ∈ BD
∴ m∠MBO = m∠NDO ⇒ (2)
∵ BD intersects MN at O
∴ m∠MOB = m∠NOD ⇒ (3) (vertically opposite angles)
From (1) , (2) and (3)
∴ ΔBOM ≅ ΔDON
∴ OM = ON
