Plane Geometry - Bruce E. Shapiro
Plane Geometry - Bruce E. Shapiro Plane Geometry - Bruce E. Shapiro
110 SECTION 22. NEUTRAL GEOMETRY« CC BY-NC-ND 3.0. Revised: 18 Nov 2012
Section 23Angle-Side-AngleTheorem 23.1 (ASA (Angle Side Angle)) If triangles △ABC and△DEF satisfy (see figure 23.1)Then △ABC ∼ = △DEF .∠CAB ∼ = ∠F DEAB ∼ = DE∠ABC ∼ = ∠DEFFigure 23.1: Angle-Side-Angle.Proof. By the ruler postulate there exists a point G ∈ −→ AC such that AG ∼ =DF (see figure 23.2).Then by SAS△ABG ∼ = △ABC (23.1)111
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Section 23Angle-Side-AngleTheorem 23.1 (ASA (Angle Side Angle)) If triangles △ABC and△DEF satisfy (see figure 23.1)Then △ABC ∼ = △DEF .∠CAB ∼ = ∠F DEAB ∼ = DE∠ABC ∼ = ∠DEFFigure 23.1: Angle-Side-Angle.Proof. By the ruler postulate there exists a point G ∈ −→ AC such that AG ∼ =DF (see figure 23.2).Then by SAS△ABG ∼ = △ABC (23.1)111
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