A triangle ABC is right angled at A. L is a point on BC such that AL BC. Prove that BAL = ACB.


It is given to us –


ΔABC is a right - angled triangle.


A = 90°


L is a point on BC


AL BC


We have to prove BAL = ACB.


We know that the sum of the angles of a triangle is equal to 180°. Thus, in ΔABC,


BAC + B + C = 180° - - - - (i)


Now, in ΔABL,


AL BC, i.e., ALB = 90°


Since, the sum of the angles of a triangle is equal to 180°,


BAL + ALB + B = 180° - - - - (ii)


From equation (i) and equation (ii), we can say that


BAC + B + C = BAL + ALB + B


C + BAC = BAL + ALB


C = BAL (Since, A = 90° and ALB = 90°, so they are equal)


BAL = ACB


Hence, proved.


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