论文部分内容阅读
在解决求角度的问题时,倘若灵活地运用数学思想,便能使问题化难为易.一方程思想例1如图1,在△ABC中,∠C=∠ABC=2∠A,BD是AC边上的高.求∠DBC的度数.分析:设∠A=x°,然后用含x的代数式表示出∠C和∠ABC的度数,从而根据三角形的内角和等于180°构造方程.解:设∠A=x°,则∠C=∠ABC=2x°.在△ABC中,∠A+∠C+∠ABC=180°,所以x+2x+2x=180,解得x=36.所以∠C=72°.在Rt△BDC中,∠DBC=90°-72°=18°.
In solving the problem of seeking angles, if the flexible use of mathematical thinking, we can make the problem difficult.Estimate Equation Example 1 as shown in Figure 1, △ ABC, ∠C = ∠ABC = 2∠A, BD is AC Analysis: Suppose ∠A = x ° and then express the degrees of ∠C and ∠ABC using the algebraic formula with x, so as to construct the equation according to the interior angle of the triangle and equal to 180 ° Solution: Let ∠C = ∠ABC = 2x ° for ∠A = x °. In △ ABC, ∠A + ∠C + ∠ABC = 180 °, so x + 2x + 2x = 180, so that x = 36. So ∠C = 72 °. In RtΔ BDC, ∠DBC = 90 ° -72 ° = 18 °.