你了解平行四边形的其他性质吗?

• 作 者: 张云玲
• 出 处: 中学生数理化(八年级数学)(配合人教社教材)
• 发表日期: 2013年04期
• 关键词: 三角形面积 胡朋 公共边 直角边 君上

1.平行四边形内任意一点与四个顶点的连线所分得的四个三角形中,相对的三角形面积之和相等.已知(?)ABCD中,点O是其中任意一点,连接AO、BO、CO、DO,则S_(△AOD)+S_(△BOC)=S_(△AOB)+S_(△DOC).证明:如图1,过O分别作OE⊥AD于E,OF⊥BC于F,OM⊥AB于M,ON⊥DC的延长线于N.因为AB∥DC,AD∥BC,所以点E、O、F,点M、O、N分别在同一直线上.

1. In the parallelogram, the area of ​​the opposite triangle is equal to the sum of the areas of the triangles divided by the connection of any point in the parallelogram with the four vertices. It is known that (?) ABCD, point O is any one of them, and AO, BO (△ AOD) + S △ (△ BOC) = S △ AOB + S △ (DOC). Proof: As shown in Figure 1, over O were made OE⊥AD in E, OF⊥BC in F, OM ⊥ AB in M, ON ⊥ DC extension line in N. Because AB ∥ DC, AD ∥ BC, so the point E, O, F, points M, O, N are on the same line.