Plane Geometry - Bruce E. Shapiro

SECTION 37. AREA 189Proof. (Exercise.)Definition 37.10 Let T be a triangular region corresponding to △ABC.Drop a perpendicular from C to ←→ AB and call the foot of the perpendicularD. Then we definebase(T ) = ABheight(T ) = CDFigure 37.3: Definition of base and height of any triangle. Pick any edgeof the triangle (such as AB). Then the length of AB is called the base ofthe triangle, and the distance from AB to its opposite vertex C is calledthe height of the triangle.Theorem 37.11 Let T be a triangle. ThenÅ 1α(T ) = base(T ) × height(T )2ãProof. (Exercise.)Theorem 37.12 Suppose that △ABC ∼ △DEF . Thenα(△DEF ) = r 2 α(△ABC)where r = DE/AB.Proof. (Exercise.)Revised: 18 Nov 2012 « CC BY-NC-ND 3.0.