Plane Geometry - Bruce E. Shapiro

106 SECTION 21. SIDE-ANGLE-SIDEFigure 21.4: Proof of the existence of perpendiculars (see theorem 21.5).the line, then C and E are on opposite sides. Hence segment CE intersectsline ←→ AB at some point F .Then △F AE ∼ = △F AC (SAS). Hence δ = µ(∠AF E) = µ(∠AF C) = γ.Since γ and δ form a linear pair, γ + δ = 180.γ = δ = 90.Hence m ⊥ l, proving existence of the perpendicular line.Hence (since γ = δ),« CC BY-NC-ND 3.0. Revised: 18 Nov 2012