Question

In the given figure ABC is an equilateral triangle and BC is produced to D such that BC=CD. prove that AD perpendicular to AB ​. Plz answer fast.

Answer 1

If ABC is an equilateral triangle and BC is produced to D such that BC=CD then DA ⊥ AB

Step-by-step explanation:

ABC is an equilateral Triangle

=> ∠ A = ∠B = ∠C = 60°

AB = BC = CA

BC is produced to D such that BC=CD

=> CA = CD

=> ∠CAD = ∠CDA

∠C = ∠ACD = ∠CAD + ∠CDA  ( Sum of Exterior angle of a triangle = Sum of opposite two angles of triangle)

=> 60° =  2 ∠CAD

=> ∠CAD = 30°

∠BAD = ∠BAC + ∠CAD

=> ∠BAD =  60° + 30°

=> ∠BAD =  90°

=> DA ⊥ AB