In △ABC, right angled at B, BO⊥AC Show that ∠1=∠2 (i e , ∠ABO=∠BCO) - Maths - Triangles

Question

I n   △ A B C ,   r i g h t   a n g l e d
  a t   B ,   B O ⊥ A C   S h o w  
t h a t   ∠ 1 = ∠ 2   ( i e ,   ∠
A B O = ∠ B C O )

Sanjari Kalantri · Accepted Answer

Dear Student,

Referring to your diagram, we have the following solution:Given: ∠B = 90°, BO⊥AC (or, ∠BOC = ∠BOA = 90°)To prove: ∠1 = ∠2
Proof: In △ABC and △AOB,∠OAB = ∠CAB   [Common]∠AOB = ∠ABC = 90°∴ By AA-similarity, △AOB~△ABC
In a pair of similar triangles, all corresponding angles are equal
Thus, ∠ACB = ∠OBA, or ∠1 = ∠2

I n △ A B C , r i g h t a n g l e d a t B , B O ⊥ A C . S h o w t h a t ∠ 1 = ∠ 2 ( i . e . , ∠ A B O = ∠ B C O )

$I n △ A B C, r i g h t a n g l e d a t B, B O ⊥ A C . S h o w t h a t ∠ 1 = ∠ 2 (i . e ., ∠ A B O = ∠ B C O)$