Plane Geometry - Bruce E. Shapiro

146 SECTION 31. QUADRILATERALS IN NEUTRAL GEOMETRYTwo quadrilaterals are congruent if all four corresponding sides and allfour corresponding angles are congruent.Figure 31.1: □ABCD is a convex quadrilateral with diagonals AC andBD; □EF QH is a non-convex quadrilateral with diagonals EG and F H;□IJKL is not a quadrilateral, although □IKJL (not shown) is a quadrilateral.You should convince yourself that the following definition of a convexquadrilateral is consistent with definition 15.1.Definition 31.2 □ABCD is convex if each vertex is contained in theinterior of the angle formed by the three other vertices (in their cyclicorder around the quadrilateral).Figure 31.2: The angle sum of a quadrilateral is equal to the sum of theangle sums of the triangles defined by either diagonal (theorem 31.4).Definition 31.3 Let □ABCD be convex. Then its angle sum is given bythe sum of the measures of its interior angles:σ(□BACD) = µ(∠ABC) + µ(∠BCD)+ µ(∠CDA) + µ(∠DAC)« CC BY-NC-ND 3.0. Revised: 18 Nov 2012