在四边形中,对角互补的四边形是一类特殊四边形,它具备如下的性质:如图1,在四边形ABCD中,若∠BAD+∠BCD=180°,则AC·BD=AB·CD+AD·BC.证明如图2,在BA的延长线上取一点E,使∠ADE=∠CDB,因为∠BAD+∠EAD=180°,∠BAD+∠BCD=180°,所以∠EAD=∠BCD,于是△EDA∽△BDC,可得AE/BC=AD/CD. In the quadrilateral, the diagonally complementary quadrilateral is a special type of quadrilateral, which has the following properties: As shown in Figure 1, in the quadrilateral ABCD, AC · BD = AB · CD + AD · if BCD + ∠BCD = 180 ° BC. Prove as shown in Figure 2, take a point E on the extension of BA, so that ∠ADE = ∠CDB, because ∠BAD + ∠EAD = 180 °, ∠BAD + ∠BCD = 180 °, so ∠EAD = ∠BCD, EDA ∽ △ BDC, available AE / BC = AD / CD.