[Script Info]
Title: 
[Events]
Format: Layer, Start, End, Style, Name, MarginL, MarginR, MarginV, Effect, Text
Dialogue: 0,0:00:00.00,0:00:03.13,Default,,0000,0000,0000,,假設有個∠ABC
Dialogue: 0,0:00:03.24,0:00:04.84,Default,,0000,0000,0000,,它看起來是這樣的
Dialogue: 0,0:00:04.95,0:00:07.32,Default,,0000,0000,0000,,角的頂點是B
Dialogue: 0,0:00:07.45,0:00:08.80,Default,,0000,0000,0000,,頂點是B
Dialogue: 0,0:00:08.91,0:00:11.50,Default,,0000,0000,0000,,假設點A在這裡
Dialogue: 0,0:00:11.61,0:00:14.36,Default,,0000,0000,0000,,點C在這裡
Dialogue: 0,0:00:14.45,0:00:18.59,Default,,0000,0000,0000,,再假設有一個∠DAB
Dialogue: 0,0:00:18.69,0:00:22.35,Default,,0000,0000,0000,,叫∠DBA吧
Dialogue: 0,0:00:22.46,0:00:24.99,Default,,0000,0000,0000,,因爲我想讓角的頂點在B
Dialogue: 0,0:00:25.11,0:00:26.89,Default,,0000,0000,0000,,假設∠DBA是這樣的
Dialogue: 0,0:00:27.00,0:00:31.61,Default,,0000,0000,0000,,點D是在這裡
Dialogue: 0,0:00:31.72,0:00:32.72,Default,,0000,0000,0000,,這就是點D
Dialogue: 0,0:00:32.83,0:00:37.11,Default,,0000,0000,0000,,假設我們已經知道∠DBA的度數
Dialogue: 0,0:00:37.21,0:00:40.45,Default,,0000,0000,0000,,假設∠DBA是40°
Dialogue: 0,0:00:40.55,0:00:41.99,Default,,0000,0000,0000,,這邊這個角
Dialogue: 0,0:00:42.11,0:00:44.82,Default,,0000,0000,0000,,它的度數是40°
Dialogue: 0,0:00:44.93,0:00:49.71,Default,,0000,0000,0000,,假設∠ABC的度數是
Dialogue: 0,0:00:49.83,0:00:55.05,Default,,0000,0000,0000,,50°
Dialogue: 0,0:00:55.14,0:00:57.53,Default,,0000,0000,0000,,好了 這有很多有意思的點
Dialogue: 0,0:00:57.65,0:00:59.87,Default,,0000,0000,0000,,第一個有趣兒的點就是
Dialogue: 0,0:00:59.97,0:01:02.90,Default,,0000,0000,0000,,這兩個角共用一條邊
Dialogue: 0,0:01:03.01,0:01:04.20,Default,,0000,0000,0000,,你可以把它們看成射線
Dialogue: 0,0:01:04.30,0:01:05.32,Default,,0000,0000,0000,,也可以看成直線
Dialogue: 0,0:01:05.42,0:01:06.21,Default,,0000,0000,0000,,還可以看成是線段
Dialogue: 0,0:01:06.29,0:01:07.68,Default,,0000,0000,0000,,但如果把它們當成射線
Dialogue: 0,0:01:07.80,0:01:10.85,Default,,0000,0000,0000,,那這兩個角共享射線BA
Dialogue: 0,0:01:10.98,0:01:13.09,Default,,0000,0000,0000,,如果有兩個角
Dialogue: 0,0:01:13.19,0:01:14.20,Default,,0000,0000,0000,,它們共用一條邊
Dialogue: 0,0:01:14.29,0:01:16.47,Default,,0000,0000,0000,,那這兩個角就是鄰角
Dialogue: 0,0:01:16.59,0:01:19.43,Default,,0000,0000,0000,,因爲“鄰”字面意思就是“旁邊”
Dialogue: 0,0:01:19.54,0:01:25.94,Default,,0000,0000,0000,,這兩個角就是鄰角
Dialogue: 0,0:01:26.07,0:01:27.84,Default,,0000,0000,0000,,你還會發現其它有意思的點兒
Dialogue: 0,0:01:27.96,0:01:28.79,Default,,0000,0000,0000,,這也很有意思
Dialogue: 0,0:01:28.90,0:01:32.14,Default,,0000,0000,0000,,我們已知∠DBA是40°
Dialogue: 0,0:01:32.26,0:01:35.01,Default,,0000,0000,0000,,∠ABC是50°
Dialogue: 0,0:01:35.11,0:01:36.29,Default,,0000,0000,0000,,那你就可以猜出
Dialogue: 0,0:01:36.41,0:01:40.73,Default,,0000,0000,0000,,∠DBC的度數了
Dialogue: 0,0:01:40.83,0:01:43.63,Default,,0000,0000,0000,,∠DBC的度數是
Dialogue: 0,0:01:43.74,0:01:45.77,Default,,0000,0000,0000,,如果你在這兒畫個量角器
Dialogue: 0,0:01:45.88,0:01:46.87,Default,,0000,0000,0000,,當然我不會畫了
Dialogue: 0,0:01:46.97,0:01:48.56,Default,,0000,0000,0000,,否則圖就亂七八糟了
Dialogue: 0,0:01:48.65,0:01:50.48,Default,,0000,0000,0000,,我還是快速畫一個
Dialogue: 0,0:01:50.57,0:01:52.33,Default,,0000,0000,0000,,假設這裡有個量角器
Dialogue: 0,0:01:52.45,0:01:54.59,Default,,0000,0000,0000,,很明顯 這個角是50°
Dialogue: 0,0:01:54.71,0:01:56.77,Default,,0000,0000,0000,,這個角是40°
Dialogue: 0,0:01:56.88,0:01:57.91,Default,,0000,0000,0000,,那你想知道
Dialogue: 0,0:01:58.02,0:02:00.30,Default,,0000,0000,0000,,∠DBC的度數
Dialogue: 0,0:02:00.40,0:02:02.12,Default,,0000,0000,0000,,它其實就是
Dialogue: 0,0:02:02.23,0:02:04.70,Default,,0000,0000,0000,,40°加上50°
Dialogue: 0,0:02:04.78,0:02:06.21,Default,,0000,0000,0000,,把這些東西都擦掉
Dialogue: 0,0:02:06.30,0:02:07.32,Default,,0000,0000,0000,,讓圖看得更清楚點兒
Dialogue: 0,0:02:07.42,0:02:09.78,Default,,0000,0000,0000,,因此∠DBC的度數
Dialogue: 0,0:02:09.90,0:02:12.70,Default,,0000,0000,0000,,就是90°
Dialogue: 0,0:02:12.79,0:02:15.49,Default,,0000,0000,0000,,我們知道90°的角是個特殊的角
Dialogue: 0,0:02:15.58,0:02:21.65,Default,,0000,0000,0000,,這個角是直角
Dialogue: 0,0:02:21.78,0:02:27.91,Default,,0000,0000,0000,,若兩角之和爲90°
Dialogue: 0,0:02:28.01,0:02:30.39,Default,,0000,0000,0000,,這兩角互爲余角
Dialogue: 0,0:02:30.50,0:02:32.01,Default,,0000,0000,0000,,我們也可以說
Dialogue: 0,0:02:32.13,0:02:42.46,Default,,0000,0000,0000,,∠DBA和∠ABC是互余
Dialogue: 0,0:02:42.57,0:02:49.84,Default,,0000,0000,0000,,因爲它們度數之和爲90°
Dialogue: 0,0:02:49.98,0:02:56.78,Default,,0000,0000,0000,,因此∠DBA加上∠ABC
Dialogue: 0,0:02:56.90,0:02:59.87,Default,,0000,0000,0000,,等於90°
Dialogue: 0,0:02:59.99,0:03:02.76,Default,,0000,0000,0000,,它們相加 組成了一個直角
Dialogue: 0,0:03:02.87,0:03:04.56,Default,,0000,0000,0000,,這又是一個
Dialogue: 0,0:03:04.67,0:03:07.14,Default,,0000,0000,0000,,與直角相關的術語
Dialogue: 0,0:03:07.25,0:03:10.86,Default,,0000,0000,0000,,當組成一個直角時
Dialogue: 0,0:03:10.96,0:03:13.32,Default,,0000,0000,0000,,組成直角的這兩條射線
Dialogue: 0,0:03:13.43,0:03:15.51,Default,,0000,0000,0000,,或者是組成直角的兩條直線
Dialogue: 0,0:03:15.69,0:03:17.43,Default,,0000,0000,0000,,或者是組成直角的兩條線段
Dialogue: 0,0:03:17.54,0:03:19.00,Default,,0000,0000,0000,,是相互垂直的
Dialogue: 0,0:03:19.11,0:03:22.85,Default,,0000,0000,0000,,因爲我們知道∠DBC是90°
Dialogue: 0,0:03:22.94,0:03:25.65,Default,,0000,0000,0000,,或者∠DBC是直角
Dialogue: 0,0:03:25.76,0:03:32.20,Default,,0000,0000,0000,,這就告訴了我們
Dialogue: 0,0:03:32.29,0:03:35.58,Default,,0000,0000,0000,,我可以說
Dialogue: 0,0:03:35.70,0:03:46.15,Default,,0000,0000,0000,,線段DB與BC垂直
Dialogue: 0,0:03:46.27,0:03:50.41,Default,,0000,0000,0000,,我們甚至可以說射線BD
Dialogue: 0,0:03:50.51,0:03:53.94,Default,,0000,0000,0000,,我們不用 垂直 這個詞了
Dialogue: 0,0:03:54.05,0:03:56.69,Default,,0000,0000,0000,,有時也可以用這個符號
Dialogue: 0,0:03:56.77,0:03:58.45,Default,,0000,0000,0000,,它就表示兩條直線垂直
Dialogue: 0,0:03:58.54,0:04:02.55,Default,,0000,0000,0000,,DB與BC垂直
Dialogue: 0,0:04:02.66,0:04:05.42,Default,,0000,0000,0000,,這些都是真命題
Dialogue: 0,0:04:05.53,0:04:07.92,Default,,0000,0000,0000,,都是從DB與BC組成的角
Dialogue: 0,0:04:08.02,0:04:10.30,Default,,0000,0000,0000,,推斷出來的
Dialogue: 0,0:04:10.41,0:04:13.68,Default,,0000,0000,0000,,這是90°的角
Dialogue: 0,0:04:13.78,0:04:15.34,Default,,0000,0000,0000,,當兩個角相加爲其它度數時
Dialogue: 0,0:04:15.45,0:04:18.48,Default,,0000,0000,0000,,我們還有其它的術語
Dialogue: 0,0:04:18.59,0:04:20.45,Default,,0000,0000,0000,,就比如
Dialogue: 0,0:04:20.55,0:04:24.95,Default,,0000,0000,0000,,這裡有個角 I
Dialogue: 0,0:04:25.04,0:04:27.38,Default,,0000,0000,0000,,我就現編一個
Dialogue: 0,0:04:27.50,0:04:29.76,Default,,0000,0000,0000,,我們叫這個角
Dialogue: 0,0:04:29.86,0:04:37.06,Default,,0000,0000,0000,,我們用字母 XYZ 來標記這個角
Dialogue: 0,0:04:37.17,0:04:44.64,Default,,0000,0000,0000,,假設∠XYZ是60°
Dialogue: 0,0:04:44.74,0:04:48.31,Default,,0000,0000,0000,,再假設還有一個角
Dialogue: 0,0:04:48.42,0:04:52.11,Default,,0000,0000,0000,,它是這樣的
Dialogue: 0,0:04:52.20,0:05:01.74,Default,,0000,0000,0000,,我用MNO表示這個角
Dialogue: 0,0:05:01.83,0:05:06.88,Default,,0000,0000,0000,,假設∠MNO是120°
Dialogue: 0,0:05:06.99,0:05:09.23,Default,,0000,0000,0000,,如果這兩個角相加
Dialogue: 0,0:05:09.34,0:05:10.78,Default,,0000,0000,0000,,我把這個寫下來
Dialogue: 0,0:05:10.87,0:05:23.50,Default,,0000,0000,0000,,∠MNO加∠XYZ
Dialogue: 0,0:05:23.61,0:05:25.33,Default,,0000,0000,0000,,等於
Dialogue: 0,0:05:25.44,0:05:29.70,Default,,0000,0000,0000,,等於120°加60°
Dialogue: 0,0:05:29.80,0:05:32.42,Default,,0000,0000,0000,,就是180°
Dialogue: 0,0:05:32.53,0:05:34.56,Default,,0000,0000,0000,,如果把這兩個角相加
Dialogue: 0,0:05:34.64,0:05:37.73,Default,,0000,0000,0000,,你就可以繞圓走半圈
Dialogue: 0,0:05:37.84,0:05:41.09,Default,,0000,0000,0000,,或者是繞整個半圓
Dialogue: 0,0:05:41.18,0:05:43.11,Default,,0000,0000,0000,,或者是半圓形量角器
Dialogue: 0,0:05:43.22,0:05:46.79,Default,,0000,0000,0000,,如果兩角之和爲180°
Dialogue: 0,0:05:46.90,0:05:48.73,Default,,0000,0000,0000,,它們就是補角
Dialogue: 0,0:05:48.83,0:05:50.93,Default,,0000,0000,0000,,我知道這有點難記
Dialogue: 0,0:05:51.04,0:05:52.43,Default,,0000,0000,0000,,90°是余角
Dialogue: 0,0:05:52.54,0:05:54.22,Default,,0000,0000,0000,,有兩個角互余
Dialogue: 0,0:05:54.31,0:05:56.21,Default,,0000,0000,0000,,如果之和是180°
Dialogue: 0,0:05:56.32,0:06:03.11,Default,,0000,0000,0000,,就是補角
Dialogue: 0,0:06:03.23,0:06:05.94,Default,,0000,0000,0000,,如果這兩個角還相鄰
Dialogue: 0,0:06:06.05,0:06:08.06,Default,,0000,0000,0000,,它們共用一條邊
Dialogue: 0,0:06:08.18,0:06:09.91,Default,,0000,0000,0000,,讓我在這兒畫
Dialogue: 0,0:06:10.02,0:06:13.46,Default,,0000,0000,0000,,假設有這樣一個角
Dialogue: 0,0:06:13.58,0:06:15.18,Default,,0000,0000,0000,,還有這樣一個角
Dialogue: 0,0:06:15.28,0:06:17.81,Default,,0000,0000,0000,,讓我標一些字母
Dialogue: 0,0:06:17.92,0:06:19.26,Default,,0000,0000,0000,,我又從新使用ABC
Dialogue: 0,0:06:19.36,0:06:23.56,Default,,0000,0000,0000,,這就是 ABC
Dialogue: 0,0:06:23.66,0:06:26.05,Default,,0000,0000,0000,,還有一個角是這樣的
Dialogue: 0,0:06:26.16,0:06:30.62,Default,,0000,0000,0000,,還有一個角是這樣的
Dialogue: 0,0:06:30.73,0:06:32.72,Default,,0000,0000,0000,,我已經用了C
Dialogue: 0,0:06:32.83,0:06:34.73,Default,,0000,0000,0000,,看起來是這樣的
Dialogue: 0,0:06:34.85,0:06:37.07,Default,,0000,0000,0000,,注意 我再說一遍
Dialogue: 0,0:06:37.19,0:06:39.33,Default,,0000,0000,0000,,這個角是50°
Dialogue: 0,0:06:39.44,0:06:42.37,Default,,0000,0000,0000,,這個角是130°
Dialogue: 0,0:06:42.51,0:06:47.27,Default,,0000,0000,0000,,很明顯 ∠DBA加∠ABC
Dialogue: 0,0:06:47.49,0:06:48.55,Default,,0000,0000,0000,,如果把它們相加
Dialogue: 0,0:06:48.65,0:06:50.63,Default,,0000,0000,0000,,130°加50°
Dialogue: 0,0:06:50.74,0:06:52.07,Default,,0000,0000,0000,,等於180°
Dialogue: 0,0:06:52.18,0:06:53.38,Default,,0000,0000,0000,,因此它們互補
Dialogue: 0,0:06:53.49,0:06:54.83,Default,,0000,0000,0000,,我把這個寫下來
Dialogue: 0,0:06:54.95,0:07:04.13,Default,,0000,0000,0000,,∠DBA和∠ABC互補
Dialogue: 0,0:07:04.25,0:07:07.47,Default,,0000,0000,0000,,因爲它們之和是180°
Dialogue: 0,0:07:07.60,0:07:10.59,Default,,0000,0000,0000,,而且它們還是鄰角
Dialogue: 0,0:07:10.71,0:07:13.89,Default,,0000,0000,0000,,它們是相鄰的
Dialogue: 0,0:07:14.01,0:07:16.63,Default,,0000,0000,0000,,因爲它們互補且相鄰
Dialogue: 0,0:07:16.74,0:07:18.78,Default,,0000,0000,0000,,如果你看這個大角
Dialogue: 0,0:07:18.89,0:07:21.53,Default,,0000,0000,0000,,也就是除了共用那條邊外的兩邊組成的角
Dialogue: 0,0:07:21.65,0:07:28.25,Default,,0000,0000,0000,,如果你看∠DBC
Dialogue: 0,0:07:28.37,0:07:30.74,Default,,0000,0000,0000,,它們實際上組成了一條直線
Dialogue: 0,0:07:30.84,0:07:36.98,Default,,0000,0000,0000,,我們可以稱它爲平角
Dialogue: 0,0:07:37.09,0:07:38.93,Default,,0000,0000,0000,,我給大家介紹了很多詞了
Dialogue: 0,0:07:39.04,0:07:40.87,Default,,0000,0000,0000,,我們已經有了很多基礎
Dialogue: 0,0:07:40.97,0:07:44.39,Default,,0000,0000,0000,,可以用來進行有趣的證明
Dialogue: 0,0:07:44.50,0:07:46.21,Default,,0000,0000,0000,,在回顧一下
Dialogue: 0,0:07:46.31,0:07:50.15,Default,,0000,0000,0000,,我們講了鄰角
Dialogue: 0,0:07:50.26,0:07:54.72,Default,,0000,0000,0000,,所有兩角之和爲90°的角都是互余
Dialogue: 0,0:07:54.85,0:07:56.28,Default,,0000,0000,0000,,這之和是90°
Dialogue: 0,0:07:56.40,0:07:58.13,Default,,0000,0000,0000,,如何它們還相鄰的話
Dialogue: 0,0:07:58.26,0:08:01.97,Default,,0000,0000,0000,,它們外邊的兩條邊還組成一個直角
Dialogue: 0,0:08:02.07,0:08:04.05,Default,,0000,0000,0000,,如果有直角了
Dialogue: 0,0:08:04.16,0:08:08.97,Default,,0000,0000,0000,,直角的兩條邊就相互垂直
Dialogue: 0,0:08:09.08,0:08:12.12,Default,,0000,0000,0000,,如果兩角之和爲180°
Dialogue: 0,0:08:12.23,0:08:14.20,Default,,0000,0000,0000,,它們就互補
Dialogue: 0,0:08:14.32,0:08:16.17,Default,,0000,0000,0000,,如果它們還相鄰
Dialogue: 0,0:08:16.29,0:08:18.23,Default,,0000,0000,0000,,就會構成一條直線
Dialogue: 0,0:08:18.36,0:08:19.56,Default,,0000,0000,0000,,換種說法就是
Dialogue: 0,0:08:19.65,0:08:20.89,Default,,0000,0000,0000,,如果有一個平角
Dialogue: 0,0:08:21.02,0:08:23.57,Default,,0000,0000,0000,,有其中一個角
Dialogue: 0,0:08:23.68,0:08:26.01,Default,,0000,0000,0000,,另外一個角就跟它互補
Dialogue: 0,0:08:26.13,0:08:28.08,Default,,0000,0000,0000,,它們之和等於180°
Dialogue: 0,0:08:28.19,0:08:28.98,Default,,0000,0000,0000,,今天就講到這裡