角平分线与等腰三角形是一对难舍难分的好朋友.事实上,我们遇到等腰三角形时,常会想到顶角的平分线;遇到角平分线时,又往往会想到构造等腰三角形.下面举例说明它们的联系.一、角平分线+平行线?等腰三角形角平分线遇上平行线时,会产生等腰三角形.例1如图1,已知点C为∠AOB的平分线上一点,CD//OB交于OA于点D.求证OD=CD Angle bisector and isosceles triangle is a good friend for a long time .In fact, when we encounter the isosceles triangle, we often think of the bisector of the apex angle. When we meet the angle bisector, we often think of the structure Waist triangle. The following examples illustrate their connection. First, the angle bisector + parallel lines? Isosceles triangle angle bisector meets the parallel lines, will produce isosceles triangle .Example 1 As shown in Figure 1, known point C is ∠ AOB Point bisector, CD / OB to pay at OA at point D. Verification OD = CD