1.4平行线的判定课件2025-2026学年 浙教版七年级数学下册

第1章 相交线与平行线 1.4 平行线的判定（1） 课堂小结 随堂演练 获取新知 知识回顾 例题精讲 知识回顾 填表： 截线 被截线 形状（英文字母） 同位角 内错角 同旁内角 同旁 同侧 F 异侧 之间 Z 同旁 之间 U 获取新知 说一说：用三角尺和直尺画平行线的方法. l2 l1 一放，二靠，三推，四画. （1）在画图过程中，怎样操作才能使画出的直线是l2//l1? （2）把图中的直线l1，l2看成被尺边AB 所截，那么在画图过程中，三角尺起了使什么角始终保持相等的作用？ l2 l1 同位角 由此你能发现判定两直线平行的方法吗? 基本事实：两条直线被第三条直线所截，如果同位角相等，那么这两条直线平行. 同位角相等，两直线平行 平行线的判定定理（1） 两条直线被第三条直线所截，如果同位角相等，那么这两条直线平行. 符号言语： 因为∠1= ∠2 所以l1//l2(同位角相等，两直线平行) 已知直线l 和直线外一点P,如图所示.用三角尺和直尺画四条和直线l 平行的直线,并要求过P点 l 你能用同位角的方法做出来吗？ 全品文教 (批注) - 回顾第一节的内容，想一想用所学知识，还有没有其他方法去画这个平行线 在资源包里面添加安装备课助手 例题精讲 例1：如图所示，已知直线l1，l2被直线l3所截，∠1=45°，∠2=135°. 判断l1与l2是否平行，并说明理由. 解：l1//l2.理由如下： 如图所示，∠1与∠3是直线l1，l2被直线l3所截的一对同位角. 由已知，得∠2+∠3=180°， 所以∠3=180°-∠2=180°-135°=45°. 又因为∠1=45°， 所以∠1=∠3. 根据“同位角相等，两直线平行”，得l1//l2. 例2：如图所示，AB⊥EF，CD⊥EF，E，F 分别为垂足. 直线AB 与CD 平行吗？请说明理由. 解：AB//CD.理由如下： 由已知AB⊥EF,CD⊥EF， 根据垂直的意义，得∠1=∠2=Rt∠. 所以AB//CD ( ). 同位角相等，两直线平行 在同一平面内，垂直于同一条直线的两条直线互相平行. 课堂小结 平行线的判定 定义 __________相等，两直线平行 在同一平面内，垂直于同一条直线的两条直线__________ 用三角尺和直尺画平行线 同位角 互相平行 随堂演练 1. 如图,在平移三角尺画平行线的过程中,理由是 (　　) A.两直线平行,同位角相等 B.两直线平行,内错角相等 C.同位角相等,两直线平行 D.内错角相等,两直线平行 C 2. 已知在同一平面内有三条不同的直线a,b,c,下列说法错误的是 (　　) A.如果a∥b,a⊥c,那么b⊥c B.如果b∥a,c∥a,那么b∥c C.如果b⊥a,c⊥a,那么b⊥c D.如果b⊥a,c⊥a,那么b∥c C 3.如图,已知∠1+∠3=180°,请说明a∥b. 解:因为∠1+∠2=180,∠1+∠3=180°, 所以∠2=∠3, 所以a∥b. 第1章 相交线与平行线 1.4 平行线的判定（2） 课堂小结 随堂演练 获取新知 知识回顾 例题精讲 知识回顾 如何判断两条直线平行？ 同位角相等，两直线平行. 在同一平面内，垂直于同一条直线的两条直线互相平行. 获取新知 探究1：如图所示，直线AB，CD 被直线EF 所截. 若∠2=∠3，则AB 与CD 平行吗? （1）上节课，我们已经有怎样的判定两直线平行的方法？ 两条直线被第三条直线所截，如果同位角相等，那么这两条直线平行. （2）由“∠2=∠3”，能得出有一对同位角相等吗? 因为 ∠1=∠3（对顶角相等） ∠2=∠3（已知） 所以 ∠1=∠2（等量代换） 所以 AB //CD （同位角相等，两直线平行） 两条直线被第三条直线所截，如果内错角相等，那么这两条直线平行. 内错角相等，两直线平行 平行线的判定定理（2） 两条直线被第三条直线所截，如果内错角相等，那么这两条直线平行. 符号言语： 因为∠1= ∠3 所以l1//l2(内错角相等，两直线平行) 例题精讲 例1：如图所示，AC⊥CD 于点C，∠1与∠2互余.判断AB，CD 是否平行，并说明理由. 解：AB//CD.理由如下： 如图所示，由已知AC⊥CD， 根据互余的意义，得∠2与∠3互余. 又已知∠1与∠2互余， 根据“同角的余角相等”，得∠1=∠3. 根据“内错角相等，两直线平行”，可得AB//CD. 如图所示，直线AB，CD 被直线EF 所截. 若∠3+∠4=180 ° ，易知AB 与CD 平行. 想一想，为什么? 因为 ∠2+∠4＝180 ° （平角定义） ∠3+∠4＝180 ° （已知） 所以 ∠2=∠3（等量代换） 所以 AB //CD （内错角相等，两直线平行） 两条直线被第三条直线所截，如果同旁内角互补，那么这两条直线平行. 同旁内角互补，两直线平行 平行线的判定定理（3） 两条直线被第三条直线所截，如果同旁内角互补，那么这两条直线平行. 符号言语： 因为∠1+∠4＝180 ° 所以l1//l2(同旁内角互补，两直线平行) 判定两直线平行的方法 (1)当已知两条直线的交点个数,可用定义法判定; (2)当待判定的两条直线与第三条直线相交,可抓住所成角的位置与特殊性判定:①同位角相等,两直线平行;②内错角相等,两直线平行;③同旁内角互补,两直线平行; (3)若两条直线在同一平面内都垂直于第三条直线,则可用“在同一平面内,垂直于同一条直线的两条直线互相平行”来判定. 例2：如图所示，AP 平分∠BAC，CP 平分∠ACD， ∠1+∠2=90°.判断AB，CD 是否平行，并说明理由. 解：AB//CD.理由如下： 已知AP 平分∠BAC，CP 平分∠ACD， 根据角平分线的意义，知 ∠1＝∠BAC， ∠2＝∠ACD， 所以∠BAC+∠ACD=2(∠1+∠2)=2×90°=180°. 根据“同旁内角互补，两直线平行”，得AB//CD. 课堂小结 平行线的判定 同位角相等，两直线平行 内错角_______，两直线平行 同旁内角________，两直线平行 定义 相等 互补 随堂演练 1. 如图,若∠A=∠D,则AB∥CD,判断依据是(　　) A.两直线平行,同位角相等 B.两直线平行,内错角相等 C.同位角相等,两直线平行 D.内错角相等,两直线平行 D 2.如图,若∠1=100°,∠4=80°,则　　　　∥　　　　,理由是　　　　　　　　　　　 ;若∠3=70°,则∠2=　　　　°时,可推出AB∥CD. AB CD 同旁内角互补,两直线平行 110 3.如图所示,AC⊥BC于点C,∠1与∠2互余.由这些条件能够判定哪两条直线平行?请说明理由. [解析] 由垂直的定义可知∠ACB=90°,又知∠1与∠2互余,可得∠2与∠ACD互补,推出AB∥CD. 解:AB∥CD.理由如下: 因为AC⊥BC,所以∠ACB=90°. 因为∠1与∠2互余,所以∠1+∠2=90°, 所以∠2+∠ACB+∠1=180°,即∠2+∠ACD=180°, 所以AB∥CD(同旁内角互补,两直线平行). huohua_res/6u2XE0q4R/css/app.14a2614d.css [data-v-272193f8]{outline:none;-webkit-tap-highlight-color:rgba(0,0,0,0)}.fade-enter-active[data-v-272193f8],.fade-leave-active[data-v-272193f8]{-webkit-transition:opacity .4s;transition:opacity .4s}.fade-enter[data-v-272193f8],.fade-leave-to[data-v-272193f8]{opacity:0}.tooltip-wrapper[data-v-272193f8]{position:absolute;width:-webkit-fit-content;width:-moz-fit-content;width:fit-content;-webkit-transition-property:left,top;transition-property:left,top;-webkit-transition-duration:.4s;transition-duration:.4s;-webkit-transition-timing-function:ease-out;transition-timing-function:ease-out;font-family:-apple-system,BlinkMacSystemFont,Helvetica Neue,PingFang SC,Microsoft YaHei,Source Han Sans SC,Noto Sans CJK SC,WenQuanYi Micro 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