Question

in the given figure a b perpendicular to BC, d e perpendicular to AC and GS perpendicular to BC prove that triangle ABC is similar to triangle GCF

Answer 1

In triangle ABC and triangle ADE,
Angle A = Angle A (common)
Angle DAE = Angle BAC
Therefore by AA criterion for similarity,
Triangle ABC is similar to Triangle AED

In triangle ABC and triangle CFD,
Angle C = Angle C (common)
Angle GFC = Angle ABC
Therefore by AA criterion for similarity,
Triangle ABC is similar to Triangle GFC

Since Triangle ADE and Triangle GCF is similar to triangle ABC,
Triangle ADE is similar to Triangle GCF
Hence, Proved.

Answer 2

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