Maths-
General
Easy

Question

In straight triangle space ABC right angled at  A, AL is drawn perpendicular to BC. Prove that straight angle BAL equals straight angle ACB.

hintHint:

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  straight capital delta  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 straight capital delta  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

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