Question

a triangle abc is a right angle truangle at a al drawn perpendicular to nc. prove that angle bal = angle acb

Answer 1

In ΔALB

<ALB + <BAL + < ABL = 180°

[Angle sum property of a triangle]

⇒ 90° + <BAL + <ABC = 180°

⇒ <BAL + <ABC = 90° ..........(i)

In ΔABC,

<BAC + <ACB + <ABC = 180

[Angle sum property of a triangle]

⇒ 90 + <ACB + <ABC = 180

⇒ <ACB + < ABC = 90 ..........(ii)

From (i) and (ii), we get

⇒ <BAL + <ABC = <ACB + <ABC

Hence, <BAL = <ACB