Question

tell 19 fast and correct

Answer 1

hello,
given that BC║DA,BC=DA
therefore ∠OCB=∠ODA(alternate angles for parallel lines BC,AD)
inΔOAD and ΔOBC,
∠AOD=∠BOC(verticaly opposite angles are equal)
BC=AD(given)
∠OCB=∠ODA(shown above)
∴ΔOAD≡ΔOBC(AAS congruency)
⇒OC=OD (CPCT,corresponding parts of congruent triangles)
but OC+OD=CD
∴O is the midpoint of CD
⇒OA=OB(CPCT)
but OA+OB=AB
∴O is the midpoint of AB
hence proved 
hope this helps,if u like it please mark it as brainliest

Answer 2

In triangle AOD and triangle BOC

BC || AD

angle OAD = angle OBC
angle ODA = angle OCB

[alternate interior angles]

also BC=AD

therefore, triangle OAD congruent to triangle OBC

therefore OA=OB & OD=OC
therefore O is the mid point of AB & CD