Question

The bisectors of base angles of a triangle cannot enclose a right angle in any case. 

 

Answer 1

In a ABC
Sum of all angles of triangles is `180^@` 

i.e, `∠ A+∠ B+∠C =180^@` divide both sides by `2` 

⇒ `1/2∠A+1/2∠B+1/2∠C=180^@` 

⇒`1/2∠A+∠OBC+∠OBC=90^@`      [∵ OB,OC insects ∠B and ∠C]

 

⇒`∠OBC+∠OCB=90^@-1/2A` 

Now in `Δ OCB=180^@`  

`∴ ∠ BOC+∠OBC+∠OCB=180^@` 

⇒`∠ BOC+90^@-1/2∠A=180^@` 

⇒ `∠ BOC=90^@-1/2 ∠A` 

Hence, bisectors of a base angle cannot enclose right angle.