Question

triangle ABC is right angled at B. BD is perpendicular to AC. Prove that triangle BDC is similar to triangle ABC.

Answer 1

above photo is my answer

Answer 2

Answer with Step-by-step explanation:

As shown in attached figure Δ ABC is right angled at B and BD is perpendicular to AC

Consider Δ ABC and Δ BDC

∠ABC = ∠BDC                      (each 90° as BD is perpendicular to AC)

∠C = ∠C                                 (common)

∴ Δ ABC  ≈  Δ BDC               (Angle- angle )

Hence  Δ ABC  is  similar to  Δ BDC by angle angle criteria.