做数学题时所依据的条件必须是真实可靠的,如定义、定理、公理、公式、法则等,而有一些同学在做题时,常常把一些未经证明的“想当然”的结论拿来即用,导致计算或证明的过程不完整,甚至是错误的计算与证明。现撷取几例分析。一、想当然的虚假结论例1:如图(1),在△ABC 中,AB>AC,E 是∠BAC 平分线 AD 上一点,且 BE>EC,求证:AB-AC>BE-CC The conditions on which mathematics questions are based must be true and reliable, such as definitions, theorems, axioms, formulae, rules, etc., while some students often take unproven conclusions of “take it for granted” Come to use, resulting in incomplete or even erroneous calculations and proofs. Now draw a few cases of analysis. I. Taken for granted false conclusions Example 1: As shown in Figure (1), in △ABC, AB>AC,E is a point on the ∠BAC bisector AD, and BE>EC, verification: AB-AC>BE-CC