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vladimir2022 [97]
3 years ago
7

...............................................

Mathematics
1 answer:
olga2289 [7]3 years ago
3 0

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 ofBA (given)

⇒TA≅TB (Definition of midpoint)

TO≅TO (Reflexive)

Therefore, ΔBOT≅ΔAOT (by SAS criteria ):

conditions:

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