Question

AB is perpendicular to BC, DE is perpendicular to AC and GF is perpendicular to BC. Prove that Triangle ADE is similar to Triangle GCF.

Answer 1

In tri. ADE and tri. GCF
angle ABC =90°
by angle sum property of triangle
angle ABC + angle BAC + angle BCA=180°
angle BAC + angle BCA = 90°
angle BAC = angle BCA = 45°•••••• (eq 1.)
angle AED = angle GFC •••••••(each of 90°)
angle DAE = angle GCF••••••••(each of 45°)
tri. ADE ~ tri. GCF ••••••(by AA similarity criteria )
hence proved

Answer 2

Answer:

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