Question

In triangle ABC angle=90° B is joined to D the mid point of AC and produced to E such that BD=DF . EC is joined Show that angle BCE=90°.

Answer 1

Answer:

In triangle ABC and BEC

BE=AC ( given)

BC=BC ( Common)

AB=EC (given)

triangle ABC is congrent to triangle BEC

so,

angle ABC = angle BCE ( Corresponding parts

of congrent )

triangle ABC+ BCE =180°

90° + BCE = 180°

BCE = 180° - 90

BCE = 90°

hence proved !