根据附件图片内容，讲解 等面积转换模型---等面积法转换 **方法总结** **1. 等面积法** | 类型 | 条件 | 图示 | 结论 | | :------- | :----------------------------------------------------------------------------------------------- | :--------------------------------------------------------------------- | :------------------------------------------------------------------------------------------------------------------------------ | | | 在△ABC 中, AD ⊥ BC, BE ⊥ AC, CF ⊥ AB | [Diagram shows triangle ABC with altitudes AD, BE, CF intersecting.] | S_(△ABC) = (1/2) * BC * AD = (1/2) * AB * CF = (1/2) * AC * BE | | | 在△ABC 中, AB=AC, D 为 BC 边上任意一点, BE ⊥ AC, DF ⊥ AB, DG ⊥ AC | [Diagram shows isosceles triangle ABC with D on BC, altitudes BE, DF, DG.] | DF + DG = BE | **2. 常见的等积转换** (1) 直角三角形斜边上的高等于两直角边的乘积除以斜边; (2) 等边三角形内部任意一点到三边的距离之和等于等边三角形的高; (3) 菱形的高等于对角线乘积的一半除以底边; (4) 三角形的内切圆半径等于三角形面积的两倍与周长的商. **方法应用** **例 1** **问题描述:** 如图, 在矩形 ABCD 中, AB=3, AD=4, 对角线 AC, BD 交于点 O, 点 P 在 AB 上, PE ⊥ AC 于点 E, PF ⊥ BD 于点 F, 则 PE+PF 的值为 **图示描述:** * Type: Geometric figure (Rectangle with diagonals and perpendiculars from a point on one side). * Main Elements: * Rectangle ABCD. * Vertices A, B, C, D labeled counterclockwise starting from top left. * Diagonals AC and BD intersect at point O. * Point P is on side AB. * Line segment PE perpendicular to AC, with E on AC. A right angle symbol is shown at E. * Line segment PF perpendicular to BD, with F on BD. A right angle symbol is shown at F. * Labels and Annotations: * Sides labeled implicitly by vertices AB, BC, CD, DA. * Length AB = 3. * Length AD = 4. * Points A, B, C, D, O, P, E, F are labeled. * "例 1 题目图" below the figure. **选项:** A. 7/5 B. 12/5 C. 13/5 D. 14/5 **关键点点拨:** 已知过同一点的两条线段分别垂直于三角形的两边, 考虑将三角形分割为两个小三角形, 结合等面积法转换求线段长.