Question

IN THE FIGURE IN ATTACHMENT, DB AND AC PERPENDICULAR TO BC AND DE PERPENDICULAR TO AB. PROVE ΔBDE SIMILAR TO ΔABC

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Answer 1

DB is parallel to AC and Ab intersects,
angle DBE in triangle DBE = angle BAC in triangle ABC as these are alternate angles        ----------------(1)

angle DEB i triangle DBE = angle ACB in triangle ABC (both 90) ---(2)

Therefore all the angles of triangles BDE and ABC are equal.
Hence these triangles are similar.

Answer 2

In triangle ΔABC and ΔBDE ,
              Angle BAC= Angle DBE       ,[ BD is parallel to AC ,(alternative angle) ]
              Angle ABC = Angle BED = 90    ,(Given) 
 if two angles of two tringle are equal corresponding then those third angle are also be equal .
so,   Angle ABC = Angle BDE 
therefore ΔABC is similar to ΔBDE   [ By AAA  similarity]