Question

Triangle ABC is right angled at a and AL perpendicular bc prove that angle bal=angle acb

Answer 1

∆ABC is right angled at A.

=> hypotenuse is BC.

we have:-

AL perpendicular to BC.

Now in ∆ABL & ∆ACL we have :

i)side AC ~ side AB (hypotenuse)

ii)side AL is common

iii)angle ALB=angle ALC (since 90°)

=>these two triangles are similar by RHS (right angled hypotenuse side) similarity.

=> angle BAL = angle ACB