Maths-

General

Easy

Question

# In right angled at A, AL is drawn perpendicular to BC. Prove that .

Hint:

### Find ∠ABC From sum of angles in triangle ABC

and Find ∠BAL From sum of angles in triangle A B l.

## The correct answer is: Hence proved

In ABC ,

∠BAC + ∠ABC + ∠ACB = 180°(sum of angles in the triangle)

∠ABC + ∠ACB= 180°- 90°(given, ∠ BAC = 90° )

∠ABC + ∠ ACB = 90°

∠ABC = 90°- ∠ ACB

In ABL ,

∠BAL + ∠ABC + ∠ ALB = 180°(sum of angles in the triangle)

∠BAL + ∠ABC= 180°- 90°(given, ∠ ALB = 90° )

∠BAL + ∠ABC = 90°

∠BAL = 90°- ∠ ABC

Substitute ∠ABC = 90°- ∠ACB in the above equation

∠BAL = 90°- (90°- ∠ ACB)

∴ ∠ BAL = ∠ ACB

Hence proved

In ABL ,

Hence proved

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