In ∆GKH, KG = KH; P is any point on line GH not in segment GH. Prove that PK is always greater than either KG or KH.

Question

Answer 1

angle KGH = angle H (isosceles triangle)

angle P + angle PKG = angle KGH (exterior angle) = angle H

therefore angle P < angle H

and therefore PK > KH triangle with unequal angles, larger side opposite larger angle