Answer:
- OT⊥BA;T is the midpoint of BA-------Given
- ∠BTO and ∠ATO are right angles ---Definition of perpendicular lines
- ∠BTO≅∠ATO---------------------------------All right angles are congruent
- T is the midpoint of BA------------------ Given
- TA≅TB-------------------------------------------Definition of midpoint
- TO≅TO------------------------------------------Reflexive
- ΔBOT≅ΔAOT---------------------------------SAS
Step-by-step explanation:
Given that [tex]OT[/tex]⊥[tex]BA[/tex] and [tex]T[/tex] is the midpoint of [tex]BA[/tex]
As [tex]OT[/tex]⊥[tex]BA[/tex],
∠[tex]BTO[/tex] and ∠[tex]ATO[/tex] are right angles (Definition of perpendicular lines)
⇒∠[tex]BTO[/tex]≅ ∠[tex]ATO[/tex] (All right angles are congruent)
T is the midpoint of[tex]BA[/tex] (given)
⇒[tex]TA[/tex]≅[tex]TB[/tex] (Definition of midpoint)
[tex]TO[/tex]≅[tex]TO[/tex] (Reflexive)
Therefore, Δ[tex]BOT[/tex]≅Δ[tex]AOT[/tex] (by SAS criteria ):
conditions:
- [tex]BT=AT(side)[/tex]
- ∠[tex]BTO=[/tex]∠[tex]ATO(angle)[/tex]
- [tex]TO=TO(side)[/tex]
