Find x :

In the triangle ABC, BD bisects angle B and is perpendicular to AC. If the lengths of the sides of the triangle are expressed in terms of x and y as shown, find the values of x and y.

In triangle ABC; ∠A = 60°, ∠C = 40° and bisector of angle ABC meets side AC at point P. Show that BP = CP.

In the given figure, AB ⊥ BE, EF ⊥ BE, AB = EF and BC = DE, then :

1. △ ABD ≅ △ EFC

2. △ ABD ≅ △ FEC

3. △ ABD ≅ △ ECF

4. △ ABD ≅ △ CEF