Question

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Answer 1

Answer:

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

Step-by-step 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:

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