25. Exercise Problem XVII

\(∆ ABC\) and \(∆ DBC\) are two isosceles triangles on the same base \(BC\) and vertices \(A\) and \(D\) are on the same side of \(BC\) (see Fig. 7.39).

 

 

If \(AD\) is extended to intersect \(BC\) at \(P\), show that

 

(i) \(∆ ABD ≅ ∆ ACD\)

 

(ii) \(∆ ABP≅ ∆ ACP\)

 

(iii) \(AP\) bisects \(∠ A\) as well as \(∠ D\).

 

(iv) \(AP\) is the perpendicular bisector of \(BC\).