Answer:
Step-by-step explanation:
A) In ΔONE & ΔEST
ON // ST (Construction) and NS is transversal.
∠1 = ∠4 {alternate interior angles}
NE =ES {Given E is midpoint}
∠2 = ∠3 {Vertically opposite angle}
ΔONE ≅ ΔEST { A S A congruent}
OE ≅ TE {CPCT}
ON = ST {CPCT} ---------(I)
ON = OH -----------------(II)
From (I) & (II)
OH = ST & OH // ST (construction)
OHST is a parallelogram.
So, OE // HS -----------------(A)
OE = TE
OT = 2OE
OE = (1/2)OT
OE = (1/2)HS ------------------(B)
From A & B , midpoint theorem is proved
