Question

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Answer 1

1. OT⊥BA;T is the midpoint of BA-------Given
2. ∠BTO and ∠ATO are right angles ---Definition of perpendicular lines
3. ∠BTO≅∠ATO---------------------------------All right angles are congruent
4. T is the midpoint of BA------------------ Given
5. TA≅TB-------------------------------------------Definition of midpoint
6. TO≅TO------------------------------------------Reflexive
7. ΔBOT≅ΔAOT---------------------------------SAS

Explanation:

Given that
`OT`⊥
`BA` and
`T` is the midpoint of
`BA`

As
`OT`⊥
`BA`,

∠
`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)

Therefore, Δ
`BOT`≅Δ
`AOT` (by SAS criteria ):

conditions:

• 
  `BT=AT(side)`
• ∠
  `BTO=`∠
  `ATO(angle)`
• 
  `TO=TO(side)`